# Worksheet: Acceleration over a Distance

In this worksheet, we will practice using an object's initial and final velocities and the object's displacement to define acceleration by using the formula v² = u² + 2as.

**Q4: **

An object starts from rest and accelerates at a rate of 2 m/s^{2}
along a straight line until its velocity reaches 8 m/s.
How far has the object traveled from its starting position when it reaches this velocity?

**Q5: **

An object has an initial velocity of 3 m/s and accelerates
in the direction of its velocity along a straight line at a rate of 4 m/s^{2}. Its velocity reaches 11 m/s when it is at the end of the line. What is the length of the line?

**Q6: **

An object has an initial velocity that decreases to 10 m/s as the object accelerates in the opposite direction to its velocity. The object moves along a 60 m long straight line accelerating with a magnitude of 6.5 m/s^{2}. What is the object’s initial velocity to the nearest meter per second?

**Q7: **

A large bird has to run while flapping its wings to launch
itself into the air. The bird needs to be running at 5.745 m/s to start to fly.
If the bird can accelerate at 1.65 m/s^{2}, how far must it run before
it can take off? Give your answer to one decimal place.

**Q8: **

A game is played where coins are slid along a 2.5 m long tabletop and must stop as close to the end of the table as possible. Two coins are launched at the same time as each other, and the coins are decelerated by friction at 0.25 m/s^{2}. One of the coins stops exactly at the end of the table and the other stops 10 cm from the end of the table.

How many centimeters per second greater is the initial velocity of the coin that reaches the end of the table than that of the coin that stops short? Answer to two significant figures.

How many seconds pass between the coin that stops short coming to rest and the coin that reaches the end of the table coming to rest? Answer to two significant figures.

**Q9: **

A jet aircraft’s engines accelerate it at an average rate of 0.6 m/s^{2}
as it travels the length of a m
long runway. If the aircraft was stationary at the beginning of the runway, what is the aircraft’s speed at the end of the runway, to the nearest meter per second?

**Q10: **

A passenger in an airport luggage reclaim area notices her luggage moving toward her on a carousel. She walks toward the luggage at 0.3 m/s, parallel to the carousel, picks it up, and moves a distance of 0.15 m against the direction of the carousel. After that, she continues walking at 0.1 m/s, parallel to the carousel. What is her rate of acceleration in the direction of the carousel while picking up the luggage?

**Q11: **

A person on water skis is floating at rest in the water,
holding a handle attached to a tow rope. The other end of the rope is
attached to a speedboat 10 m in front of the skier, which is also at rest. The
tow rope’s length is 20 m, and the skier will not start to be pulled by the
rope until the distance between the boat and the skier has become 20 m. The boat
accelerates away from the skier at a steady 6.5 m/s^{2}. What will the velocity of the boat be when the rope starts to pull the skier? Round your answer to one decimal place.

**Q12: **

A motorcycle moving at a velocity of 20 m/s along a road drives into a large patch of mud that stretches for 5 m and continually reduces the motorcycle’s velocity while the motorcycle drives through it. The velocity of the motorcycle when it has completely driven through the mud is 15 m/s. What was the average acceleration of the motorcycle while driving through the mud?

**Q13: **

An object starts from rest and accelerates along an 8 m long straight line. Its velocity reaches 12 m/s when it is at the end of the line. What is the object’s acceleration rate along the line?

**Q14: **

What formula correctly relates the change in the velocity of an object from its initial velocity to its final velocity , the acceleration of the object, and the displacement of the object in the direction of its acceleration?

- A
- B
- C
- D
- E

**Q15: **

A ball rolls down a slope and increases its speed, as shown in the diagram. The ball’s speed does not decrease as it rolls horizontally.

What is the average acceleration of the ball along the slope? Round your answer to two decimal places.

How many seconds after does the ball reach a point 25 m horizontally away from the base of the slope? Assume that the horizontal speed of the ball is the same as the ball’s speed at the base of the slope. Round your answer to one decimal place.

How far does the ball roll along the slope? Round your answer to two decimal places.

**Q16: **

A train is traveling at 15 m/s and then accelerates at 0.5 m/s^{2} while traveling 750 m in the direction of its acceleration.

What is the train’s speed after accelerating? Answer to one decimal place.

For how long does the train accelerate? Answer to one decimal place.

**Q17: **

A bullet fired from a gun leaves the end of the 55 cm long gun barrel at a speed of 500 m/s and hits a bottle 35 m away, as shown in the diagram.

What is the average acceleration of the bullet in the gun barrel? Round your answer to the nearest kilometer per square second.

How much time after the bullet leaves the gun does it hit the bottle, assuming it moves with a constant velocity?