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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 1: KinematicsVectors & Motion

Vectors & Motion (College Board AP® Physics 1: Algebra-Based): Exam Questions

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1
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A stone is thrown horizontally from a bridge into a pond. At the same instant, another identical stone is dropped vertically into the pond. Both stones have the same initial height.

Which of the following statements is correct?

  • Both stones hit the water at exactly the same time.

  • The stone that is thrown horizontally hits the water before the stone that is vertically dropped.

  • The stone that is vertically dropped hits the water before the stone that was thrown horizontally.

  • There is not enough information to know which stone hits the water first.

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2
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A soccer ball is kicked at an angle of 45 degree to the ground. Which of the following statements is true about the motion of the soccer ball?

  • The vertical speed of the soccer ball increases on the way up and decreases on the way down

  • The acceleration vector points in the same direction as the velocity vector on the way down and in the opposite direction on the way up

  • The velocity of the soccer ball is zero at the top of the trajectory

  • The horizontal speed of the soccer ball is constant throughout the trajectory

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3
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A train is travelling along a bridge. A passenger releases a ball out of the window.

Which of the following is the correct graph for the horizontal velocity of the ball over time?

Assume air resistance can be ignored.

Four graphs labelled A to D show voltage (V_K) against time (t). A decreases, B is constant, C increases then decreases, D increases linearly.

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    4
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    Which of the following is the magnitude of the resultant velocity for a system with horizontal velocity v subscript x space equals space 15 space straight m divided by straight s and vertical velocity v subscript y space equals space 20 space straight m divided by straight s?

    • 17.5 m/s

    • 25 m/s

    • 30 m/s

    • 35 m/s

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    5
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    A ball is thrown horizontally from a cliff with an initial velocity of 15 m/s.

    Which of the following determines how long the ball is in the air?

    • The horizontal velocity of the ball

    • The height of the cliff

    • The mass of the ball

    • The horizontal distance traveled

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    1
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    A projectile is launched with an initial velocity of magnitude M at an angle ϕ to the horizontal.

    Which of the following gives the correct expression for the time of flight of the projectile?

    • t space equals space fraction numerator space 2 M space sin space ϕ space over denominator g end fraction

    • t space equals space fraction numerator space minus space M space sin space ϕ space over denominator g end fraction

    • t space equals space fraction numerator space space 2 M space sin space ϕ space over denominator negative g end fraction

    • t space equals space M space sin space ϕ space minus space 2 g

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    2
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    An aeroplane travels to the right over an island of length 600m. Its resultant speed, v_res, points down and right at an angle θ to the direction in which the aeroplane's nose points.

    An aeroplane with a length of 50 m is travelling across an ocean when it passes over a small island. The island is 600 m wide.

    A strong wind blows the aeroplane to its right while its engines does work, such that its velocity, v subscript r e s end subscript is constant and points at an angle theta to the direction in which the aeroplane's nose points.

    Which of the following is the correct expression for the sideways distance that the aeroplane travels from when it first passes over the island to when it completely clears the island?

    • fraction numerator 600 cos theta over denominator sin theta end fraction

    • fraction numerator 650 cos theta over denominator sin theta end fraction

    • fraction numerator 600 sin theta over denominator cos theta end fraction

    • fraction numerator 650 sin theta over denominator cos theta end fraction

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    3
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    A graph with y (m) on the vertical axis and time (s) on the horizontal axis. A parabola starting at the origin with a peak at (5.0, 15) and returns to a vertical displacement of zero after 10 s.

    A projectile is fired upwards from a canon. Its vertical displacement over time is shown in the figure above.

    The same projectile is fired in the exact same way, but now a strong breeze blows in the positive horizontal direction, giving the projectile constant acceleration.

    Which of the following diagrams could be a correct path for this projectile?

    You may ignore resistive forces from the air.

    • The graph from the question with a new line. The new line has the same start and end points but a higher peak.
    • The same line as the graph in the question.
    • The same graph as in the question but skewed right, so the peak of 15 m occurs around 9 s and the line returns to y = 0 m at 12 s.
    • The same graph as in the question but skewed left so the peak of 15 m is at 3 s and the line returns to y = 0 m at 11 s.

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    4
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    A boat is travelling to the right down a river at constant velocity. On board, a performer throws a juggling ball directly upwards.

    If the ball takes 5 seconds to return to the performer, which of the following vectors is most nearly the direction of the ball's velocity after 2 seconds?

    • Upwards arrow
    • Arrow to the right
    • Diagonal arrow up and right
    • Diagonal arrow down and right

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    1
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    A rock is kicked horizontally from the edge of a 150 space straight m high cliff and lands in the water below at a distance of 90 space straight m from the base of the cliff. Which of the following is the final horizontal velocity of the rock?

    • 15 space straight m divided by straight s

    • 16 space straight m divided by straight s

    • 21 space straight m divided by straight s

    • 35 space straight m divided by straight s

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    21 mark

    A duck takes off from rest at an angle of 67 degree from the water and accelerates in this direction at a constant rate of 12.5 space straight m divided by straight s squared until a resultant velocity of 25 space straight m divided by straight s is reached. Which of the following are correct for the horizontal and vertical displacements of the duck during its period of acceleration?

    • straight capital delta x space equals space 9.8 space space straight m

      straight capital delta y space equals space 23 space straight m

    • straight capital delta x space equals space 23 space space straight m

      straight capital delta y space equals space 9.8 space straight m

    • straight capital delta x space equals space 12.4 space space straight m

      straight capital delta y space equals space 23 space straight m

    • straight capital delta x space equals space 23 space space straight m

      straight capital delta y space equals space 12.4 space straight m

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    3
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    Two projectiles are launched simultaneously with the same initial speed but at angles theta subscript 1 space equals space 30 degree and theta subscript 2 space equals space 60 degree relative to the horizontal. Which of the following is true about their horizontal ranges?

    • The range of projectile 1 is greater than projectile 2.

    • The range of projectile 2 is greater than projectile 1.

    • The ranges of both projectiles are equal.

    • The ranges depend on the vertical velocities and cannot be determined.

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    4
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    A toy glider is launched in a field with initial velocities v subscript x 0 end subscript space equals space 10 space straight m divided by straight s and v subscript y 0 end subscript space equals space 15 space straight m divided by straight s. The rocket experiences constant acceleration a subscript x space equals space 2.0 space straight m divided by straight s squared in the horizontal direction due to the thrust of its propellor.

    Which of the following is most nearly the distance between the apex of the glider's path and its initial position?

    • 11 m

    • 13 m

    • 17 m

    • 21 m

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    5
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    An arrow is fired by an archer with an initial vertical velocity component of v subscript y 0 end subscript space equals space 17.5 space straight m divided by straight s.

    At a time before the arrow reaches its maximum height, it reaches a velocity v with rightwards arrow on top, which is at an angle theta to the vertical.

    Which of the following expressions describes the horizontal distance covered by the arrow at this time?

    • open vertical bar v with rightwards arrow on top close vertical bar sin theta open parentheses fraction numerator 17.5 space plus space open vertical bar v with rightwards arrow on top close vertical bar cos theta over denominator g end fraction close parentheses space

    • open vertical bar v with rightwards arrow on top close vertical bar sin theta open parentheses fraction numerator 17.5 space minus space open vertical bar v with rightwards arrow on top close vertical bar cos theta over denominator g end fraction close parentheses space

    • fraction numerator 1225 over denominator 8 g end fraction

    • open vertical bar v with rightwards arrow on top close vertical bar cos theta open parentheses fraction numerator 17.5 space minus space open vertical bar v with rightwards arrow on top close vertical bar sin theta over denominator g end fraction close parentheses space

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