Chapter 2: Kinematics PDF

Chapter 2 :Kinematics Mrs. Pooja Brahmaiahchari Warmup session…. 1. Who is the father of scientific method? a. Albert Einstien b. Issac Newton c. Galileo Galilei d. Aristotle 2. The number of significant figures in 0.005 a. 4 b. 3 c. 2 d. 1 What is Kinematics? Kinematics is the descript...

Chapter 2 :Kinematics Mrs. Pooja Brahmaiahchari Warmup session…. 1. Who is the father of scientific method? a. Albert Einstien b. Issac Newton c. Galileo Galilei d. Aristotle 2. The number of significant figures in 0.005 a. 4 b. 3 c. 2 d. 1 What is Kinematics? Kinematics is the description of how things move. Kinematics is defined as Study of Motion without considering its cause. For example: When you are resting, your heart moves blood through your veins. Vectors -vs-Scalars A scalar is a quantity with no direction associated with it. A vector is a quantity with a magnitude and direction. Will use + and – signs to indicate vector directions Vectors are represented graphically by arrows. Vectors can be one dimensional. We will be discussing motion in one dimension. Displacement Position (length) is one of the three fundamental measurements we previously discussed. It tells where the object is at any particular time. Consider two ways to describe a change in position. Distance is a scalar. It represents the total distance travelled. If I run 4 laps around a 400m track then I have travelled a distance of 1600m. Displacement is a vector. It represents the net change in position. If I run 4 laps around a 400m track then my displacement is 0m. Figure 2.3 A professor paces left and right while lecturing. Her position relative to Earth is given by x. The displacement of the professor relative to Earth is represented by an arrow pointing to the right. Displacement Displacement is the difference between the end position and the starting position. In one dimension this can be written mathematically as: ∆𝑥 = 𝑥𝑓 − 𝑥0 ∆𝑥 is displacement, 𝑥𝑓 is the final position, 𝑥0 is the initial position. If there is a change in direction as the object moves from x1to x2 then displacement will be less than the distance travelled. 1. Calculate the displacement of the professor where the initial position is 2m and the final position is 4.5m to the right. Solution: given initial position 𝑥0 = 2m, 𝑥𝑓 = 4.5m, thus Displacement = final position –initial position ∆𝑥 = 𝑥𝑓 − 𝑥0 = 4.5m – 2.0m =2.5m Distance Distance is to be defined as the magnitude or the size of displacements between two positions. Distance travelled is total length of the path travelled between two positions. Distance has no direction, hence no sign. Speed and Velocity To describe motion, we need to add a second fundamental measure (time). If we divide a change in position by a change in time, then we get speed or velocity. How can we measure speed? Speed is a scalar. The average speed is the total distance traveled divided by the time it takes to travel the distance. 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 Speed = 𝒕𝒊𝒎𝒆 Velocity(v) is a vector. It has a magnitude and direction. Average velocity is the displacement divided by the elapsed time. Δ𝑥 𝑥𝑓 −𝑥0 𝑣ഥ = = Δ𝑡 𝑡𝑓 −𝑡0 Time, Velocity and Speed Time Velocity Speed 1.Time means change Or Change in Distance travelled by time the interval over which position(displacement) taken change occurs with respect to time 2. The SI unit for time is The SI unit for velocity is The SI unit is meters per the second, abbreviated s. meters per second or m/s, second or m/s,or km/h or km/h Vector Quantity Scalar quantity 2. Megan walks 1100m to the left in 330 s. What was her average speed in m/s?(Round the answer to two significant digits.) Instantaneous Velocity The instantaneous velocity at any moment is defined as the average velocity during infinitesimally short time interval. ∆𝑥 𝑣ҧ = , ∆𝑡 We can write the definition of instantaneous velocity, v, for one dimensional motion as ∆𝑥 𝑣 = lim ∆𝑡→0 ∆𝑡 ∆𝑥 The notation lim means the ratio is to be evaluated in the limit of ∆t approaching to ∆𝑡→0 ∆𝑡 zero. Acceleration Rate of change of Velocity, Δ𝑣 𝑣𝑓 −𝑣0 𝑎= = Δ𝑡 𝑡𝑓 −𝑡0 The SI unit for acceleration is 𝑚Τ𝑠 2. Acceleration is a vector, and thus has a both a magnitude and direction. Instantaneous acceleration is the acceleration at a specific instant in time. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration. 3. A car accelerates from rest to 20 m/s in 10 seconds. Determine the car’s acceleration! 4. A car is decelerating from 30 m/s to rest in 10 seconds. Determine car’s acceleration. 5. The truck accelerates from 15m/s to 45m/s in 5 seconds. Calculate the acceleration of the truck. 6. A sports car driver travelling at 95mi/hr slams brake and comes to rest in 4 seconds. Calculate the acceleration of car in m/s2 (1km = 0.6214 miles) Kinematic Equations for constant acceleration 𝑣−𝑣0 𝑡0 = 0 ∆𝑡 = 𝑡 𝑎ത = 𝑣 = 𝑣0 + 𝑎𝑡 𝑡 𝑥0 ≡ 𝑥( 𝑡 = 0) 𝑣0 ≡ 𝑣(𝑡 = 0) 𝑣0 +𝑣 𝑥−𝑥0 𝑎 = 𝑎ഥ = constant 𝑣= 2 = 𝑡 𝑥 = 𝑥0 + 𝑣𝑡 𝑣 +𝑣 = 𝑥0 + 0 t 2 1 2 𝑥 = 𝑥0 + 𝑣0 𝑡 + 𝑎𝑡 2 𝑣 2 = 𝑣02 + 2𝑎( 𝑥 − 𝑥0 ) These equations are VERY useful. You should memorize them.(See page 57 of the text) 7. An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50m/s2 for 40.0 s. What is its final velocity? Strategy Draw a sketch. We draw the acceleration vector in the direction opposite the velocity vector because the plane is decelerating. Identify the knowns. a= - 1.50m/s2 , t= 40 s , ∆𝑣 = 70.0 𝑚/𝑠 Identify the unknown. In this case, it is final velocity, vf Determine which equation to use. 𝑣 = 𝑣0 + 𝑎𝑡 Plug in the known values and solve. 𝑣 = 𝑣0 + 𝑎𝑡 = 70.0 m/s + (- 1.50m/s2 ) (40.0 s) = 10.0 m/s 8. A car accelerates from rest at a constant rate of 2.5 m/s2. What is the velocity of the car, 20 seconds later? 9. A bus accelerates from initial velocity of 10 m/s at constant rate 2.2m/s2. What is the final velocity of the bus after 15 seconds? 10. A car traveling at 85 km/h slows down at a constant deceleration of 0.50 m/s2. Calculate: a) the distance the car travels before it stops, b) the time it takes to stop c) the distance it travels when t = 4s Problem Solving Skills 1a-Read the problem carefully. Identify the object and the question(s). Identify which laws or principles of physics are applicable. 1b-Draw a diagram. Explicitly show your choice of coordinates. 2-Identify what quantities are given or inferred. 3-Determine what quantities need to be solved. 4-Choose equations which represent the correct laws of Physics, and which can be solved for the desired unknown values. 5-Solve the problem symbolically as far as possible. When you make your calculations, keep all significant figures. Round your final answer to match the appropriate accuracy. 6a-Think about the answer. Does it make sense? 6b-Keep careful track of units. This can help you catch many mistakes. Freely Falling Objects A freely falling object is any object moving freely under the influence of gravity alone. A very common source of constant acceleration is gravity. We will usually be assuming no air resistance and at sea level on earth. Usually choose y to be our vertical direction with +y being up. a = -g g = 9.80 m/s2 Because a is constant, we can use the 4 kinematic equations. It does not depend upon the initial motion of the object Dropped – released from rest Thrown downward Thrown upward Dropping a ball from a tower 11. A ball at an initial height of 3.0 m is dropped (no initial velocity) a)When will the ball hit the ground? b)How fast will it be travelling just before it hits the ground? Throwing a ball upward from a tower 12. A ball at a height of 3.0 m is thrown upward with a velocity of 1.0 m/s. a) When will the ball hit the ground? b) How fast will it be travelling just before it hits? 13. A person throws a ball upward into the air with an initial velocity of 15m/s. Calculate a) how high it goes and b) how long it takes to reach the maximum height.? 14. A stone is dropped from the top of the building and hits the ground 5 seconds later. How tall is the building? Graphical representation When two physical quantities are plotted against one another in such a graph, the horizontal axis is usually considered to be an independent variable and the vertical axis a dependent variable. The general form of graph , y = mx + b Here m is the slope, defined to be the rise divided by the run of the straight line. b is for the y- intercept, which is the point at which the line crosses the vertical axis.  A plot of Position-time can be used to determine the velocity of an object (the slope). A plot of velocity-time can be used to determine the acceleration of an object (the slope). Plot of velocity versus time can also be used to determine the displacement of an object. For velocity versus time graphs, the area bound by the line and the axes represents the displacement. THANK YOU