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Questions and Answers
What does it mean for an object to have uniform acceleration?
Which sequence is correct for solving a kinematics problem?
What is the acceleration of a jeepney that uniformly accelerates from rest and covers 15 m in 3.25 seconds?
During free fall, what is the approximate acceleration experienced by an object at Earth's surface?
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If a race car accelerates from 18.5 m/s to 46.1 m/s in 2.47 seconds, what are the key variables needed to find its acceleration?
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What is the minimum runway length needed for an airplane to reach a speed of 61.1 m/s while accelerating at 2.5 m/s²?
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What equation would you use to find the distance covered by an object during uniformly accelerated motion?
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What is the primary factor affecting free fall acceleration?
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A projectile moves in a linear path rather than a parabolic path.
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In projectile motion, the acceleration in the horizontal direction is zero.
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The range of a projectile is its maximum vertical displacement.
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The time of flight is defined as the total time a projectile is in the air.
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Maximum height is reached when the final velocity of the projectile is at its greatest.
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The vertical motion of a projectile can be analyzed independently from its horizontal motion.
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Air resistance has a significant effect on projectile motion in a vacuum.
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The initial velocity of a projectile can only be expressed as a single component.
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The x component of the velocity changes throughout the range of motion.
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The y-component of an object's velocity during free fall is only influenced by acceleration due to gravity.
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When an object reaches its maximum height, the y component of its velocity becomes positive.
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In a projectile motion, gravity acts against the velocity until the maximum height is reached.
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A ball kicked horizontally off a 32-meter tall building has zero initial horizontal velocity.
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An object moving at constant horizontal velocity experiences zero vertical displacement.
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The horizontal distance during projectile motion is independent of the height from which it is launched.
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An object falling from a height of 50 m will take the same time to fall as an object falling from 100 m if dropped simultaneously.
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Study Notes
Uniformly Accelerated Motion: Horizontal Dimension
- Uniform acceleration occurs when a body's velocity changes constantly over a specific time interval along a straight line.
- A technique is used to solve kinematics problems:
- Identify the four variables involved in the problem, usually three known values and one unknown.
- Choose the equation that relates these four variables.
- The steps to solve a kinematics problem:
- Identify the given values.
- Identify the variables to be found.
- Write down the equations used.
- Substitute the values into the equations.
- Determine the answers.
Sample Problems
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Sample problem 1: An airplane accelerates from rest at 5.50 m/s2 for 20.25 seconds before takeoff. Calculate the distance traveled.
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Sample problem 2: A jeepney accelerates uniformly from rest over 3.25 seconds and covers 15 meters. Calculate the jeepney's acceleration.
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Sample problem 3: A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Calculate the car's acceleration and the distance traveled.
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Sample problem 4: A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 meters. Calculate the bike's acceleration.
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Sample problem 5: An engineer is designing a runway for an airport and needs to determine:
- a. The time it takes for an airplane to reach a takeoff speed of 61.1 m/s with an acceleration of 2.5 m/s2.
- b. The minimum runway length required.
Uniformly Accelerated Motion: Vertical Dimension
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Free fall is the motion of an object falling towards a planet's surface with consantt acceleration, neglecting air resistance.
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Free fall acceleration, denoted by "ag", is due to gravity.
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At the Earth's surface, free fall acceleration is approximately -9.8 m/s2 or -32 ft./s2.
Projectile Motion
- Projectile motion is a type of motion where an object moves in a parabolic path.
- The path the object follows is called its trajectory.
- A projectile is an object thrown into the air that continues to move on its trajectory acted upon by gravity.
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Elements of Projectile Motion
- When launching, a projectile is given an initial velocity at an initial angle.
- As it travels, it displaces in two dimensions, along the horizontal and along the vertical.
- The projectile hits the earth or a target with a final velocity.
Projectile Motion Factors
- Time of flight: The entire duration the projectile is in its trajectory.
- Range: The maximum horizontal distance traveled by the projectile.
- Maximum height: The maximum vertical displacement traveled by the projectile in its trajectory.
- Initial Velocity: The initial velocity can be expressed as x and y components.
- Acceleration: In projectile motion, there is no acceleration in the horizontal direction. The acceleration in the vertical direction is due to gravity.
Horizontal Motion
- The x component of the velocity is always constant throughout the range.
- The horizontal displacement follows a linear motion.
Vertical Motion
- The y component behaves as free-fall, and thus, is only affected by the acceleration due to gravity.
- Since the velocity is usually in an upward direction, from 0 to less than 90 degrees with respect to the horizontal, then upward is positive, downward is negative.
- Before reaching the maximum height, gravity acts against the velocity, slowing it down until it reaches zero.
- After reaching the maximum height, gravity is in the same direction as the velocity, speeding it up.
When the projectile is at its maximum height
- The x component of velocity is always constant.
- The y component of velocity is zero.
- The acceleration is still (g) and not zero.
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Description
Test your understanding of uniformly accelerated motion through a series of problems. This quiz covers techniques for solving kinematics problems along a horizontal dimension, including identifying variables and applying relevant equations. Practice with sample problems to enhance your skills in calculating acceleration and distance.
