# 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.

Q1:

A train has a velocity of 35 m/s when it reduces its engine power, and after 5 seconds the train has a velocity of 11.5 m/s. What is the train’s average acceleration in its direction of motion?

Q2:

A cyclist accelerates at 2.3 m/s2. How much time is needed for the cyclist to increase their velocity by 9.43 m/s?

Q3:

An object that is accelerating at 3 m/s2 increases its velocity by 1.25 m/s. For how long does the object accelerate?

Q4:

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?

Q5:

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?

Q6:

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

• A 14 m/s2
• B 28.75 m/s2
• C 9 m/s2
• D 4.6 m/s2
• E 7 m/s2

Q7:

An aeroplane 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 aeroplane’s velocity afterwards is 263 m/s. What is the average acceleration rate of the aeroplane by the gust of wind? Round your answer to one decimal place.

• A 90.7 m/s2
• B 188.1 m/s2
• C 97.4 m/s2
• D 6.7 m/s2
• E 9.8 m/s2

Q8:

An object accelerates at 5 m/s2 for 0.25 s. How much does its velocity increase?

Q9:

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?

Q10:

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/s2 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?

Q11:

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.

Q12:

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(B)
• B(A)
• C(D)
• D(C)
• E(E)

Q13:

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 decelerates, then stops, then decelerates at a greater rate in the opposite direction to the previous acceleration, and then stops again.
• 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 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.

Q14:

The following velocity-time graph shows the change in the velocity of a car that suddenly brakes to come to a stop. Which of the other graphs shown best matches the velocity-time graph for the same car stopping on the same road conditions, where the driver has a longer reaction time?

• A C
• B B
• C D
• D A
• E E

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/s2 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.