Motion in Depth

1. The SI unit of acceleration is ____.

• m/s^2correct
• m/s
• m
• s^2

Acceleration is a change in velocity (m/s) per second, giving units of m/s^2.

2. A car speeds up from 0 to 20 m/s in 4 s. What is its acceleration?

Answer: 5 m/s^2

Acceleration is the change in velocity divided by time: 20 m/s / 4 s = 5 m/s^2.

3. What does acceleration measure?

• The rate of change of velocity with timecorrect
• The total distance travelled
• The speed at a single instant
• The force acting on an object

Acceleration is the rate at which velocity changes with time.

4. Build the defining word equation for acceleration.

Answer: acceleration equals change in velocity divided by time

Acceleration equals the change in velocity divided by the time taken, a = (v - u) / t.

5. In which of these situations is the object accelerating?

• A car speeding up in a straight linecorrect
• A ball moving in a circle at constant speedcorrect
• A car slowing to a stopcorrect
• A puck sliding at constant velocity across ice

Speeding up, slowing down, and changing direction all change the velocity vector, so all involve acceleration; constant velocity does not.

6. An object moving at a constant speed around a circular track has zero acceleration.

Answer: False

Its direction keeps changing, so its velocity changes and it is accelerating (centripetal acceleration) even at constant speed.

7. In the equation v = u + at, the letter a represents ____.

• accelerationcorrect
• area
• amplitude
• altitude

In this equation a is the acceleration acting over time t.

8. Using s = ut + (1/2) a t^2 with u = 0, a = 2 m/s^2 and t = 5 s, what distance s is travelled?

Answer: 25 m

s = 0 + (0.5 times 2 times 5 times 5) = 25 m.

9. Match each SUVAT symbol to the quantity it represents.

Answer: s = Displacement; u = Initial velocity; v = Final velocity; a = Acceleration

The SUVAT letters each stand for one quantity used to describe uniformly accelerated motion.

10. Which equation of motion links final velocity, initial velocity, acceleration and time?

• v = u + atcorrect
• s = u times t
• v = s / t
• a = F / m

The SUVAT equation v = u + at connects final velocity v, initial velocity u, acceleration a and time t.

11. Build the first equation of motion in words.

Answer: final velocity equals initial velocity plus acceleration times time

The equation v = u + at states that final velocity equals initial velocity plus acceleration multiplied by time.

12. Put the algebraic steps in order to derive v = u + at from the definition of acceleration.

Answer: Start with acceleration a = (v - u) / t -> Multiply both sides by t to get at = v - u -> Add u to both sides to get v - u + u = at + u -> Rearrange to write v = u + at

Starting from a = (v - u)/t, multiply through by t and rearrange to reach v = u + at.

13. A flat, horizontal line on a distance-time graph means the object is moving at a steady speed.

Answer: False

A horizontal distance-time line means the distance is not changing, so the object is stationary, not moving.

14. The gradient of a velocity-time graph gives the ____.

• accelerationcorrect
• speed
• distance
• time

Gradient is change in velocity over change in time, which is the acceleration.

15. On a velocity-time graph the line rises steadily from 0 to 20 m/s over 5 s. What is the acceleration (the gradient)?

Answer: 4 m/s^2

The gradient is change in velocity over time: 20 m/s / 5 s = 4 m/s^2.

16. Match each motion-graph feature to what it tells you.

Answer: Slope of a distance-time graph = Speed; Slope of a velocity-time graph = Acceleration; Area under a velocity-time graph = Distance; Flat line on a velocity-time graph = Constant velocity

Slopes and areas of motion graphs each reveal a specific quantity of the motion.

17. On a distance-time graph, what does the slope (gradient) of the line represent?

• Speedcorrect
• Acceleration
• Distance
• Time

The gradient of a distance-time graph is change in distance over change in time, which is speed.

18. Which of the following statements about motion graphs are correct?

• A horizontal line on a displacement-time graph means the object is stationary.correct
• A curved displacement-time graph indicates changing velocity (acceleration).correct
• The area under an acceleration-time graph gives the change in velocity.correct
• A steeper line on a velocity-time graph means a smaller acceleration.

A flat displacement-time line means the object is stationary, a curved one means changing velocity, and the area under an acceleration-time graph gives the change in velocity; a steeper velocity-time line means a larger, not smaller, acceleration.

19. Build the sentence describing a projectile's path.

Answer: the path of a projectile is a parabola

With only gravity acting, a projectile follows a curved path shaped like a parabola.

20. Which statements about projectile motion (ignoring air resistance) are correct?

• The horizontal velocity stays constantcorrect
• Gravity acts downward the whole timecorrect
• The path traced out is a parabolacorrect
• The horizontal velocity increases as it falls

Horizontal velocity stays constant, gravity acts downward the whole time, and the path is a parabola; the horizontal velocity does not increase.

21. Ignoring air resistance, a ball thrown horizontally and a ball dropped from the same height hit the ground at the same time.

Answer: True

Both balls have the same downward acceleration and start with zero vertical velocity, so they land together.

22. At the highest point of its path, a projectile's vertical velocity is ____.

• zerocorrect
• at its maximum
• equal to g
• doubled

The projectile stops rising for an instant at the top, so its vertical velocity there is zero.

23. A ball is dropped from rest and falls for 3 s. Using g = 9.8 m/s^2, what is its downward speed after 3 s?

Answer: 29.4 m/s

v = g times t = 9.8 m/s^2 times 3 s = 29.4 m/s.

24. For a projectile with no air resistance, how do the horizontal and vertical motions relate?

• They are independent of each othercorrect
• They always cancel each other out
• The horizontal motion controls the vertical motion
• They are always equal in size

Horizontal and vertical motions of a projectile are independent; gravity affects only the vertical part.

25. Build a true sentence about velocity.

Answer: velocity has both magnitude and direction

Unlike speed, velocity has both magnitude and direction, making it a vector.

26. A car driving around a circular track at a constant speed still has a changing velocity.

Answer: True

The direction keeps changing around the circle, so the velocity changes even though the speed is constant.

27. Velocity is defined as the rate of change of ____ with time.

• displacementcorrect
• distance
• mass
• time

Velocity is the change in displacement per unit time, which is why it is a vector.

28. A runner covers a straight-line displacement of 100 m in 20 s. What is the average velocity?

Answer: 5 m/s

Average velocity is displacement divided by time, so 100 m / 20 s = 5 m/s.

29. What is the main difference between distance and displacement?

• Displacement includes direction; distance does notcorrect
• Distance is always larger than displacement
• They are the same thing in different units
• Distance is a vector and displacement is a scalar

Displacement is the straight-line change in position with direction; distance is the total path length and has no direction.

30. Which statements about velocity (as opposed to speed) are correct?

• Velocity includes a directioncorrect
• Two equal and opposite velocities can add to zerocorrect
• Velocity can never be negative
• Velocity is measured in kilograms

Velocity is a vector: it carries a direction and opposite velocities can sum to zero, whereas speed is a non-negative scalar measured in m/s, not kg.