Physics Matters GCE O Level Textbook - Dynamics 1: Mass and Weight PDF

## Chapter 3: Dynamics 1: Mass and Weight ### What You Will Learn - What are the types of forces? - Is mass the same as weight? *** ### 3.1 What Are the Types of Forces? #### Learning Outcome - Identify and distinguish between contact forces and non-contact forces. #### Forces To move our luggage...

## Chapter 3: Dynamics 1: Mass and Weight ### What You Will Learn - What are the types of forces? - Is mass the same as weight? *** ### 3.1 What Are the Types of Forces? #### Learning Outcome - Identify and distinguish between contact forces and non-contact forces. #### Forces To move our luggage from one point to another, we can either push it or pull it. Intuitively, a force can be thought of as a push or a pull due to interaction between objects to explain changes in motion. When a force is exerted on an object, the object can start or stop moving, slow down or speed up. It can also change the direction of motion of the object. #### Types of Forces Forces are produced by the interaction between objects. Forces can be classified into two types: - **Non-contact forces**: Which do not require objects to be in contact to exist. - **Contact forces**: Which exist between objects that are in contact. #### Non-contact Forces - **Gravitational force**: The pull exerted by Earth's gravity on any object (i.e. weight). - **Electrostatic force**: The attractive (i.e. pull) or repulsive (i.e. push) forces between electric charges. - **Magnetic force**: The attractive (i.e. pull) or repulsive (i.e. push) forces between magnets. #### Contact forces - **Friction**: The force that opposes or tends to oppose motion between surfaces in contact. - **Air resistance**: the frictional force exerted by air that opposes the motion of moving objects. - **Normal force**: The push exerted by a surface on an object pressing on it - this push is always perpendicular to the surface. - **Tension**: The pull exerted by a stretched spring, string or rope on an object attached to it. *** ### 3.2 Is Mass the Same as Weight? #### Learning Outcomes - State that mass is a measure of the amount of matter in a body. - State that a gravitational field is a region in which a mass experiences a force due to gravitational attraction. - Define gravitational field strength _g_. - Recall and apply the relationship weight = mass × gravitational field strength to new situations, or to solve related problems. - Distinguish between mass and weight. **When we say that a person weighs 100 kilograms, we actually mean that the person has a body mass of 100 kilograms.** When we buy a 5-kilogram bag of rice, we are buying a bag of rice that has a mass of 5 kilograms, not a bag of rice that weighs 5 kilograms. In physics, weight and mass are two very different quantities. **In everyday language, we often misuse the term weight when we mean mass.** So, what is the difference between mass and weight? #### Mass Mass is a measure of the amount of matter in a body. Its SI unit is the kilogram (kg). Mass is a property of a body that does not change with its location or shape. The mass of a body depends on the number and composition of atoms and molecules that make up the body. It is a scalar quantity. #### Weight Do you know why objects fall to the ground after you throw them up in the air? This is because a force called weight pulls them towards Earth. This force is the gravitational pull (gravitational force or gravity) exerted by Earth. **Weight is the gravitational force acting on an object that has mass.** Its SI unit is the newton (N). Since weight is a force, it is a vector quantity with both magnitude and direction. The direction of weight is downward, i.e. towards the center of Earth. #### Gravitational Field We have learned earlier that the weight of an object with mass is due to the gravitational force acting on it. This weight is the effect of a gravitational field on a mass. **A gravitational field is a region in which a mass experiences a force due to gravitational attraction.** For example, Earth with a huge mass has a gravitational field surrounding it. Thus, any object within Earth's gravitational field will experience a force exerted by Earth on it. The gravitational force experienced is the strongest at the surface of Earth. It gets weaker further away due to a decreasing gravitational field strength. #### Gravitational Field Strength The weight of an object depends on the strength of the gravitational force acting on it. For example, an object weighs less on the moon than on Earth. This is because the moon's gravitational field strength is weaker than Earth's gravitational field strength. **Gravitational field strength _g_ is defined as the gravitational force per unit mass placed at that point.** $g = \frac{W}{m}$ Where: - _g_ = gravitational field strength (N/kg) - _W_ = weight (N) - _m_ = mass of the object (kg) On Earth, the gravitational field strength _g_ is approximately 10 N/kg. This means that a 1 kg mass on Earth's surface experiences a force of 10 N due to Earth's gravitational field. On the other hand, the same 1 kg mass on the moon experiences a gravitational force of only 1.6 N. This is because the gravitational field strength on the moon is 1.6 N/kg. Imagine if were to weigh an elephant on Earth's surface and the moon's surface. The elephant would weigh much more on Earth's surface than on the moon's surface even though its mass remains unchanged. #### Relation Between Mass and Weight From the $g = \frac{W}{m}$ equation we have W = mg . **The weight or gravitational force W acting on an object is directly proportional to its mass m.** For example, if we double the mass of the object, the weight or gravitational force acting on the object also doubles. #### Gravitational Field Strength and Acceleration Due to Gravity On Earth, the gravitational field strength _g_ near its surface is 10 N/kg. Therefore, the weight _W_ (in N) of an object of mass _m_ (in kg) is given by: $W = mg = m \times 10 \frac{N}{kg}$ If the object were to free-fall under gravity without air resistance, we can find its acceleration using the equation: $F = ma$ Where: - _F_ = resultant force (N) - _m_ = mass (kg) - _a_ = acceleration (m/s²) Consider an object of mass _m_ (in kg) free-falling under gravity without air resistance. It is free-falling at an acceleration of _a_ = _g_ = 10 m/s² due to its weight _W_ (in N). $F=ma$ $W= mg = m \times 10 \frac{m}{s²}$ By comparing equations (1) and (2), we can see that gravitational field strength near the Earth's surface $(g = \frac{W}{m} = 10 \frac{N}{kg})$ is equivalent to the acceleration of free fall $(g = \frac{W}{m} = 10 \frac{m}{s²})$. #### Common Weighing Instruments Common weighing instruments like the spring balance, bathroom scale and electronic balance measure the *weight* of an object, not its mass. These machines, however, are calibrated to give readings in grams (_g_) or kilograms (_kg_). Using these weighing instruments, an object will have different mass readings at different gravitational field strengths. For example, if an astronaut steps on a bathroom scale on the moon, the reading will be lower than the reading taken on Earth. This is because the gravitational field strength on the moon (1.6 N/kg) is less than that on Earth (10 N/kg). This means that a weighing scale calibrated for use on Earth cannot be used on the moon. The weighing scale must be calibrated to the moon’s gravitational field strength to give accurate mass measurements on the moon. #### Measurement of Mass To avoid having to calibrate weighing scales for different gravitational field strengths, the mass of an object can be measured using a beam balance. A beam balance compares the gravitational force acting on an object with that acting on standard masses. As both the object and the standard masses experience the same gravitational field strength, the mass reading taken for a given object, whether on Earth or on the moon, will be the same. ##### Table 3.1: Differences between mass and weight | Mass | Weight | |---------------------------------------------------------------------|--------------------------------------------------------------------------| | An amount of matter | A gravitational force | | A scalar quantity (i.e. has only magnitude) | A vector quantity (i.e. has both magnitude and direction) | | SI unit: kilogram (_kg_) | SI unit: newton (_N_) | | Independent of the gravitational field strength | Dependent on the gravitational field strength | | Measured with a beam balance or a calibrated electronic balance | Measured with a spring balance | #### Worked Example 3A A mobile phone has a mass of 75 g. Calculate its weight if _g_ is 10 N/kg. Answer Mass of mobile phone _m_ = 75 g = 75 x 10⁻³ kg = 0.075 kg Weight of mobile phone _W_ = _mg_ = 0.075 kg x 10 N/kg = 0.75 N #### Worked Example 3B The acceleration of free fall on the moon is 1.6 m/s². The acceleration of free fall on Earth is 10 m/s². A rock has a mass of 10 kg on Earth. Calculate the weight of the rock on: (a) Earth; (b) The moon. Answer (a) Weight of the rock on Earth = 10 kg x 10 m/s² = 100 N (b) Weight of the rock on the moon = 10 kg x 1.6 m/s² = 16 N *** ## Chapter 4: Dynamics II: Forces ### What You Will Learn - What are Newton's Laws of Motion? - What are free-body and vector diagrams? - What are some effects of resistive forces on motion? *** ### 4.1 What Are Newton's Laws of Motion? #### Learning Outcomes - Apply Newton's Laws to: - Describe the ways in which a force may change the motion of a body. - Describe the effect of balanced and unbalanced forces on a body. - Identify action-reaction pairs acting on two interacting bodies. - Recall and apply the relationship resultant force = mass x acceleration to new situations, or to solve related problems. - Show an understanding that mass is the property of a body which resists change in motion (inertia). #### Effects of a Force on the Motion of a Body We can observe how forces affect the motion of objects in sports. **A body at rest moves. | A moving body increases in speed. | A moving body decreases in speed. | A moving body changes direction.** - A stationary football moves when it is kicked. There is a change in speed. - A moving hockey ball moves faster when it is pushed. There is an increase in speed. - A descending parachutist slows down due to air resistance. There is a decrease in speed. - A moving tennis ball is returned when it is hit. There is a change in direction. In each of these four sports, when a force is applied on an object, there is a change in speed and/or direction over time. In other words, there is a change in velocity. This means that there is acceleration (or deceleration). Thus, a force can cause an object to accelerate (or decelerate). **Does this mean there are no forces acting on an object when its acceleration is zero?** Zero acceleration implies that the object can be stationary or moving with constant velocity. However, even though acceleration is zero, it does not mean there are no forces acting on it. It means that the resultant of these forces is zero. #### Balanced Forces and Newton's First Law If the resultant force acting on an object is zero, we say the forces acting on the object are balanced. - The table exerts an upward force _F_ (normal force) that pushes on the book. _F_ = _W_ (weight of book). - A force _F_ is applied on a book and it moves in a straight line across a rough table. _F_ = _f_ (frictional force between the book and the table). **Resultant force:** - The two forces acting on the book are equal but act in opposite directions. - Thus, the resultant force is zero and the book remains stationary. - As the book is at rest acceleration is zero. **Resultant force:** - The two forces acting on the book are equal but act in opposite directions. - Thus, the resultant force is zero and the book continues moving at a constant velocity. The two examples illustrate Newton's First Law of Motion (i.e. the Law of Inertia). **Newton's First Law of Motion states that every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it.** We know how an object behaves if the resultant force acting on it is zero. What if the resultant force is not zero? #### Unbalanced Forces and Newton's Second Law If the resultant force acting on an object is not zero, we say the forces acting on the object are unbalanced. In the example, the forces acting on the book are balanced and it moves at a constant velocity. If the applied force _F_ is now increased the forces that act on the book are no longer balanced and the book accelerates. If the applied force _F_ is now removed while the book is still in motion, friction is the resultant force. The resultant force causes the book to decelerate and eventually stop. **When there is a resultant force acting on an object, the object will accelerate in the direction of the resultant force.** The relationship between resultant force, mass and acceleration is described by Newton's Second Law of Motion. **Newton's Second Law of Motion states that when a resultant force acts on an object of a constant mass, the object will accelerate in the direction of the resultant force.** The product of the mass and acceleration of the object gives the resultant force. **Newton's Second Law of Motion in symbols:** $F = ma$ Where: - _F_ = resultant force (_N_) - _m_ = mass of object (_kg_) - _a_ = acceleration of object (in _m/s²_) Newton’s Second Law of Motion tells us that: - a resultant force _F_ on an object produces an acceleration _a_ - doubling the resultant force _F_ on an object doubles its acceleration _a_ - with the same resultant force _F_, doubling the mass _m_ halves the acceleration _a_. One newton is defined as the force that produces an acceleration of 1.0 m/s² on a mass of 1.0 kg. If _m_ = 1.0 kg and _a_ = 1.0 m/s², by _F_ = _ma_, _F_ = 1.0 kg x 1.0 m/s² = 1.0 kg m/s² = 1.0 N #### Worked Example 4A A boy pushes a stationary box of mass 20 kg with a force of 50 N. Calculate the acceleration of the box. (Assume that there is no friction.) * **Answer** Given: mass _m_ = 20 kg force _F_ = 50 N From Newton’s Second Law: _F_ = _ma_, where _a_ = acceleration of the box _a_ = $\frac{F}{m}$ = $\frac{50 N}{20 kg}$ = 2.5 m/s² in the direction of the applied force #### Worked Example 4B (a) A shipping container of mass 1000 kg rests on a frictionless floor. A rope pulls the container to the right, causing it to increase its speed to 20 m/s in 5 s. Calculate the tension force in the rope. (b) Subsequently, the same container is pulled by an additional leftward tension force of 5000 N. Find the resultant acceleration and state its direction. * **Answer** (a) From Newton’s Second Law, tension force _T_ = _ma_, where _a_ = acceleration produced. (b) The direction of the additional tension force is towards the left. This is opposite to the direction of the tension force of 4000 N in (a). Hence, the additional tension force is -5000 N. Given: mass _m_ = 1000 kg initial speed _u_ = 0 m/s final speed v = 20 m/s time _Δt_ = 5 s (a) _a_ = $\frac{v - u}{Δt}$ = $\frac{20 \frac{m}{s} - 0 \frac{m}{s}}{ 5 s}$ = 4 m/s² _T_ = _ma_ _T_ = 1000 kg x 4 m/s² _T_ = 4000 N (b) Resultant force _F_ = 4000 N + (-5000 N) = -1000 N _a_ = $\frac{F}{m}$ = $\frac{-1000 N}{1000 kg}$ = -1.0 m/s² The resultant acceleration is 1.0 m/s² to the left. #### Newton's Third Law When you swim in a pool, do you sometimes push your feet against the wall to push yourself forward? When you do this, you are applying Newton’s Third Law of Motion. This law indicates that forces occur in pairs. **Newton’s Third Law of Motion states that if body A exerts a force _FAB_ on body B, then body B will exert an equal and opposite force _FBA_ on body A.** - The boy’s feet exert a force _FAW_ on the pool wall by pushing against it. - The wall exerts a reaction force _FWA_ on the boy’s feet. This force pushes the boy forward. In the example, _FAW_ and _FWA_ occur as a pair. They are equal in magnitude, but act in opposite directions. _FAW_ acts on the wall, while _FWA_ acts on the boy. Thus, for every action, there is an equal and opposite reaction. #### Action-reaction Pairs - A baseball player strikes the baseball with his bat. - Force of the bat on the ball. - Force of the ball on the bat. - A basketball player aims the basketball at the net. - Force of the girl on the basketball. - Force of the basketball on the girl. - A girl runs on the horizontal ground. - The ground pushes forwards on the girl. - The girl pushes backwards on the ground. **Weight is a force exerted by gravity on every object.** Consider a book that is placed on a table. Does the force of the table on the book form an action-reaction pair with the weight of the book? In the example, we examine the forces acting on the book and the table with the book. - **The gravitational force _FE_ exerted by Earth on the book, and the upward force _F_BE exerted by the book on Earth.** - **The normal force _FTB_ by the table on the book, and the normal force _FBT_ by the book on the table.** Each action-reaction pair are equal in magnitude but act in opposite directions. Hence, the force of the table on the book does not form an action-reaction pair with the weight of the book. **Newton’s Third Law of Motion tells us four characteristics of forces:** 1. Forces always occur in pairs. Each pair is made up of an action and a reaction forces. 2. Action and reaction forces are equal in magnitude. 3. Action and reaction forces act in opposite directions. 4. Action and reaction forces act on different bodies. #### Worked Example 4C A truck engine of mass 5000 kg pulls a trailer of mass 1000 kg along a level track at an acceleration of 0.10 m/s². The resistive force acting on the truck engine is 10 N per 1000 kg. The resistive force acting on the trailer is 5 N per 1000 kg. * **Answer** (a) - acceleration _a_ = 0.10 m/s² - _T_ = tension - _R_ = resistance (b) (1) Note: Examine all the forces acting on the *trailer only*. Referring to the figure, two forces are acting on the trailer - tension _T_ and the resistance _R1_ to the trailer. For the trailer, using _F_ = _ma_, where _F_ is the resultant force on the trailer, _F_ = _ma_ _T_ - _R1_ = _ma_ _T_ = _ma_ + _R1_ _T_ = 1000 kg x 0.10 m/s² + 5 N _T_ = 105 N (2) Note: Examine all the forces acting on the *engine only*. Referring to the figure, three forces are acting on the engine - the forward thrust _F_ exerted by the engine, tension _T_, and the resistance _R_ on the engine. For the engine, using _F_ = _ma_, _F_ - _T_ - _R_ = _ma_ _F_ = _ma_ + _T_ + _R_ _F_ = 5000 kg x 0.10 m/s² + 105 N + (5 x 10 N) _F_ = 655 N #### Inertia Imagine you are on a safari in Africa when a big elephant suddenly comes charging at you. To escape the charging elephant, should you run in a straight line or in a zigzag manner? The answer may seem obvious, but what is the reasoning behind it? To explain it, we need to understand inertia and how it is related to mass. The inertia of an object refers to the reluctance of the object to change its state of rest or motion, due to its mass. **Mass is the property that resists the change in motion (inertia).** An object with a greater mass will have greater inertia. In other words, the larger the mass of an object, the harder it will be for the object to: - start moving - slow down - move faster - change direction This explains why it is harder for an elephant to chase you in a zigzag manner. In fact, if the elephant tries to do that, it will probably trip and fall! Inertia also explains why people should wear seat belts. If the driver suddenly applies the brakes, he will continue to move forward due to his inertia. Without a seat belt holding him back, he would crash into the windscreen. A seat belt provides the necessary opposing force that stops him. #### Worked Example 4D An object _O_ weighing 6.0 N hangs from the end of a string _OC_ that is pulled sideways by a force _F_. The string _OC_ makes an angle of 30° with the vertical, as shown in the figure. The tension _T_ has a magnitude of 7.0 N. Given that the resultant force is zero, determine the magnitude of the *force F*. Since the resultant force is zero, the object is in equilibrium. In other words, the three arrows representing the forces form a closed triangle. * **Answer** - Using a scale of 1 cm: 1 N, draw force vector _W_. - Draw force vector _T_, with a 30° angle between the vectors _W_ and _T_. - Since the object is in equilibrium (resultant force is zero), the arrows representing the forces _W_, _F_ and _T_ result in a closed triangle. Draw force vector _F_ to complete the triangle. By measurement, the length of _F_ is 3.5 cm, so force _F_ has a magnitude of 3.5 N #### Worked Example 4E A window cleaner drops a sponge from a window at time _t_ = 0 s. The figure shows the velocity-time graph for the motion of the sponge. * **Answer** (a) From A to B, the velocity of the sponge increases uniformly and the acceleration is constant at 10 m/s². From B to D, the velocity is still increasing but at a decreasing rate. The acceleration decreases. After D, the acceleration soon becomes zero and terminal velocity of 12 m/s is reached. (b) Displacement = area under velocity-time graph = (½ x 0.6 s) x (6.0 m/s) = 1.8 m #### Worked Example 4F A box is dropped from a helicopter. The mass m of the box is 5.0 kg. * **Answer** (a) When the box is released from rest, the only initial force acting on the box is the weight of the box. Thus, the box accelerates downwards at 10 m/s². As the box falls, the air resistance it experiences increases. The resultant force is now less than the weight of the box. The box still accelerates, but the acceleration is less than 10 m/s². Air resistance increases with the increase in velocity. Eventually, the air resistance balances the weight of the box. The resultant force decreases to 0 N, and the box falls at terminal velocity (i.e. zero acceleration). (b) When the box is released from rest, the only initial force acting on the box is the weight of the box. Thus, the box accelerates downwards at 10 m/s². (c) (d) #### Vector Diagrams In Chapter 1, we have learnt how to add two vectors by the graphical method. We can apply what we have learnt to find the resultant force when three forces act on an object in two dimensions. Consider three forces acting on a block. The figure describes how we can obtain the resultant force acting on the block. **Step 1**: Choose an appropriate scale. Draw an arrow to represent one of the forces. **Step 2**: From A, draw arrow _AB_ to represent the 5 N force. The head of the arrow _OA_ is joined to the tail of arrow _AB_. **Step 3:** From _B_, draw arrow _BC_ to represent the 3 N force. The head of the arrow _AB_ is joined to the tail of arrow _BC_. **Step 4:** Join _O_ (i.e. the tail of the 4 N force) to _C_ (i.e. the head of the 3 N force). The resultant force is represented by arrow _OC_. To obtain its: - **Magnitude:** Measure the length of _OC_. - **Direction:** Measure the angle of _OC_ and the horizontal baseline. The resultant force on the block has a magnitude of 9.1 N, and acts at an angle of 42° to the horizontal. Alternatively, the resultant force (_OC_) can also be found by first finding the resultant of the 4 N force (_OA_) and 5 N force (_AB_) as an intermediate step. **Step 1:** Choose the appropriate scale. Draw _OA_ and _AB_ to represent the 4 N and 5 N forces, respectively. **Step 2:** Join _O_ to _B_ to form arrow _OB_. _OB_ represents 8.17 N, the intermediate resultant force of _OA_ and _AB_. **Step 3:** From B, draw an arrow _BC_ to represent the 3 N force. The head of the arrow _OB_ is joined to the tail of arrow _BC_. **Step 4:** Join _O_ (i.e. the tail of the 8.17 N force) to _C_ (i.e. the head of the 3 N force). The same resultant force represented by arrow _OC_ is obtained. #### Objects Falling Without Air Resistance An object can only be in free fall if the only force acting on it is its own weight. The figure shows the path taken by a feather and by a hammer falling in a vacuum (i.e. in free fall). - The velocity of the two objects under gravity increases by 10 m/s every second. That is, both objects undergo a constant acceleration of 10 m/s². - The direction of their motion is downward (i.e. towards the center of Earth). - The acceleration of the free-falling objects does not depend on their mass or size. In other words, all objects fall freely at a constant acceleration of 10 m/s². #### Objects Falling with Air Resistance When you run fast, do you feel air brushing against you? You are experiencing air resistance. It has the following characteristics: - It always opposes the motion of moving objects. - It increases with the speed of the objects. - It increases with the surface area (or size) of the objects. - It increases with the density of air. #### Terminal Velocity Small dense objects, such as steel balls, fall through air at the same acceleration and hit the ground at the same time. This is because they experience low air resistance. In comparison, a piece of paper is light and has a large surface area. It experiences greater air resistance. The paper falls at a lower acceleration. Objects experience higher air resistance when their speed increases. **When the air resistance acting against an object equals its weight, the object starts to travel at a constant speed known as terminal velocity.** This means that the object has zero acceleration. If an object falls through a short distance, it may not reach terminal velocity before hitting the ground. #### Worked Example 4E A window cleaner drops a sponge from a window at time _t_ = 0 s. The figure shows the velocity-time graph for the motion of the sponge. * **Answer** (a) From A to B, the velocity of the sponge increases uniformly and the acceleration is constant at 10 m/s². From B to D, the velocity is still increasing but at a decreasing rate. The acceleration decreases. After D, the acceleration soon becomes zero and terminal velocity of 12 m/s is reached. (b) Displacement = area under velocity-time graph = (½ x 0.6 s) x (6.0 m/s) = 1.8 m #### Worked Example 4F A box is dropped from a helicopter. The mass _m_ of the box is 5.0 kg. * **Answer** (a) When the box is released from rest, the only initial force acting on the box is the weight of the box. Thus, the box accelerates downwards at 10 m/s². As the box falls, the air resistance it experiences increases. The resultant force is now less than the weight of the box. The box still accelerates, but the acceleration is less than 10 m/s². Air resistance increases with the increase in velocity. Eventually, the air resistance balances the weight of the box. The resultant force decreases to 0 N, and the box falls at terminal velocity (i.e. zero acceleration). (b) When the box is released from rest, the only initial force acting on the box is the weight of the box. Thus, the box accelerates downwards at 10 m/s². (c) (d) #### Let’s Map It - **Forces (SI unit: N)** - Affects **motion of objects** - Is governed by - **Newton’s First Law of Motion:** Every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it. - **Newton’s Second Law of Motion:** When a resultant force acts on an object of constant mass, the object will accelerate in the direction of the resultant force. _F = ma_ where: - _F_ = resultant force (_N_) - _m_ = mass (_kg_) -_ a_ = acceleration ( _m/s²_ ) - **Newton’s Third Law of Motion:** If body A exerts a force _FAB_ on body B, then body B will exert an equal and opposite force _FBA_ on body A. - Describes **action-reaction pairs** - Applies to - **Balanced forces for a body:** - At rest - Moving at a constant velocity - **Unbalanced forces for a body:** - Accelerating - Decelerating - Is related to **inertia**, which is the property of a body which resists change in motion - **Inertia** - Is quantified by **mass of the object**: (i.e. greater the mass of the object, greater the inertia) - Without air resistance, an object falls with constant acceleration. - With air resistance, an object falls with decreasing acceleration and may reach terminal velocity. ***