# Worksheet: Acceleration over Time

In this worksheet, we will practice analyzing the motion of objects that change their velocity in some amount of time, by using the formula for acceleration, a = ∆v/∆t.

**Q4: **

An object that is accelerating at 3 m/s^{2} increases its velocity by
1.25 m/s. For how long does
the object accelerate?

**Q5: **

An object increases its velocity by 2 m/s in a time of 1.25 s. What is the object’s acceleration in that time?

**Q6: **

The change in velocity of an object over a 4-second time interval is shown in the graph. What is the acceleration of the object?

**Q7: **

An initially stationary car starts to drive forward. After 2.5 seconds, the car has a velocity of 11.5 m/s. What is the car’s average forward acceleration?

**Q8: **

An airplane flying at a velocity of 245 m/s is hit by a strong tailwind. The gust of wind lasts for 2.7 seconds and the airplane’s velocity afterward is 263 m/s. What is the average acceleration rate of the airplane by the gust of wind? Round your answer to one decimal place.

**Q10: **

The change in velocity of an object over a 4-second time interval is shown in the graph.

What is the acceleration of the object?

How many times faster does the object move at s than at s?

**Q11: **

A rocket is flying upward at a constant speed when it ejects its empty first stage boosters
and activates its second stage boosters. When this happens, the rocket has a net upward
acceleration of 15 m/s^{2} in its
direction of travel. The second stage boosters burn for 7 seconds. At the end of the burn, the rocket’s
upward velocity is 250 m/s. What velocity did the rocket have before firing the second stage
boosters?

**Q12: **

Values of an object’s velocity at different times are shown by the graph.

What is the object’s average acceleration between and ?

What is the object’s average acceleration between and ?

What is the object’s average acceleration between and ?

What is the object’s average acceleration between and ? Answer to one decimal place.

**Q13: **

Select the velocity-time graph that best matches the following description of motion:

A boat moves at constant speed through the water, then accelerates for a short time, and then continues moving at a higher constant speed.

- A(C)
- B(B)
- C(A)
- D(E)
- E(D)

**Q14: **

Which of the following descriptions best matches the motion plotted in the velocity-time graph shown?

- AAn object decelerates, then stops, then decelerates at a greater rate, and then stops again.
- BAn object moves at a constant speed, then stops, then starts moving at a lower constant speed, and then stops again.
- CAn object accelerates in the opposite direction to its velocity, then moves at a constant speed, then accelerates in the opposite direction that it accelerated before and at a lower rate, and then moves at a greater constant speed.
- DAn object accelerates in the opposite direction to its velocity, then moves at a constant speed, then accelerates in the same direction that it accelerated before but at a greater rate, and then moves at a greater constant speed.
- EAn object decelerates, then stops, then decelerates at a greater rate in the opposite direction to the previous acceleration, and then stops again.

**Q15: **

The velocity of a car at different times is shown in the diagram. The car is accelerating uniformly.

Find .

Find .

Find .

**Q16: **

Which of the following formulas correctly relates the change in the velocity of an object , the acceleration of the object, and the time for which the object accelerates ?

- A
- B
- C
- D
- E

**Q17: **

100 m
from the end of a race, a runner running at 7 m/s
accelerates by 4 m/s^{2} for 0.25 s.

What is the runner’s speed after accelerating?

How many more seconds would the runner have needed to run for him to reach the end of the race if he had not accelerated? Round your answer to one decimal place.

**Q18: **

A ball that is held at rest above the ground is released. The positions of the ball at 0.1 s intervals after its release are shown in the diagram. The changes in the positions and velocities of the ball as it falls are shown in the graph.

Which line represents the speed at which the ball falls at a given time?

- AThe blue line
- BThe orange line
- CNeither line

Which line represents the distance that the ball has fallen at a given time?

- AThe orange line
- BThe blue line
- CNeither line

Another graph shows the changes in the positions and the velocities of the dropped ball at 1 s intervals after its release. Which line represents the distance that the ball has fallen at a given time?

- ANeither line
- BThe red line
- CThe green line

**Q19: **

Which of the following is a unit of acceleration?

- Am
^{2}/s - B(m/s)
- Cm/s
^{2} - Dm
^{2}/s^{2} - Em/s

**Q20: **

Two cars accelerate along a straight road for a time of 5 seconds. The table shows the values of the velocities of the cars at 1-second time intervals.

Time in Seconds | Velocity in m/s of Car I | Velocity in m/s of Car II |
---|---|---|

1 | 10 | 15 |

2 | 14 | 18 |

3 | 18 | 21 |

4 | 22 | 24 |

5 | 26 | 27 |

Which car has the greater speed at the end of the 5 seconds?

- ACar II
- BThe cars have the same speed at the end of the 5 seconds.
- CCar I

Which car has the greater acceleration during the 5 seconds?

- AThe cars have the same acceleration.
- BCar II
- CCar I

**Q21: **

A car accelerates, starting at the time . The velocity of the car at 2 s intervals after it starts to accelerate is shown in the diagram.

What is the velocity of the car at ?

What is the acceleration of the car?

**Q22: **

Which of the following must be zero when the acceleration of an object is zero?

- AThe time the object takes in motion
- BThe speed of the object
- CThe distance travelled by the object
- DNone of the answers is correct.

**Q23: **

A boat, initially at rest, starts to move in a straight path with uniform acceleration. The average velocity of the boat during 15 s is 3 m/s. Calculate its instantaneous velocity 20 s after it starts moving.

- A11 m/s
- B8 m/s
- C7 m/s
- D4 m/s

**Q24: **

An object starts its motion from rest and moves at a uniform acceleration. The average velocity of that object is 5 m/s at time . Calculate the average velocity of that object at time .

- A40 m/s
- B15 m/s
- C10 m/s
- D20 m/s

**Q25: **

Calculate the time required for a plane to change its speed by 8 m/s if it is moving in a
straight line with an acceleration of 4 m/s^{2}.

- A2 s
- B s
- C s
- D1 s