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In this lesson, we will learn how to analyze 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 skydiver accelerates downward at a rate of 9.8 m/s^{2}. How much does their downward velocity increase in 0.67 seconds? Round your answer to two decimal places.

Q3:

A cyclist accelerates at 2.3 m/s^{2}. How much time is needed for the cyclist to increase their velocity by 9.43 m/s?

Q4:

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 𝑡 = 4 s than at 𝑡 = 0 s?

Q5:

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?

Q6:

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?

Q7:

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?

Q8:

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

Q9:

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?

Q10:

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.

Q11:

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?

Q12:

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?

Q13:

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.

Q14:

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

What is the object’s average acceleration between 𝑡 = 2 s and 𝑡 = 3 s ?

What is the object’s average acceleration between 𝑡 = 1 s and 𝑡 = 2 s ?

What is the object’s average acceleration between 𝑡 = 1 s and 𝑡 = 3 s ?

What is the object’s average acceleration between 𝑡 = 0 s and 𝑡 = 3 s ? Answer to one decimal place.

Q15:

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.

Q16:

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

Find 𝑣 1 .

Find 𝑣 2 .

Find 𝑣 3 .

Q17:

An object accelerates at 5 m/s^{2} for 0.25 s. How much does its velocity increase?

Q18:

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

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