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Worksheet: Kinematics


A particle moves along a line, accelerating at 3.6 m/s2.

If the particle’s initial velocity is 4.2 m/s, at what time is its displacement 9.3 m?

What is the particle’s velocity in the direction of its acceleration at the time that its displacement is 9.3 m?


In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, of 295.38 km/h. The one-way course was 8.00 km long. Acceleration rates are often described by the time it takes to reach 96.0 km/h from rest. If this time was 4.00 s and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the course?


Two trains are moving at 30 m/s in opposite directions on the same track. The engineers see simultaneously that they are on a collision course and apply the brakes when they are m apart. Assuming both trains have the same acceleration, what must this acceleration be if the trains are to stop just short of colliding?


While entering a freeway, a car accelerates from rest at a rate of 2.40 m/s2 for 12.0 s.

How far does the car travel in those 12.0 s?

What is the car’s final velocity?


A cyclist travels from point A to point B in 7.0 min. At point A the cyclist is at rest. During the first 1.4 min of her trip, she maintains a uniform acceleration of 0.072 m/s2. She then travels at constant velocity in the same direction for the next 3.2 min. She decelerates at a constant rate and comes to rest at point B 2.4 min later.

What is the acceleration during the last 3.0 mins of travel?

What distance does the cyclist travel?


An object has an acceleration of 1.2 cm/s2. At , its velocity is cm/s.

Determine the object’s velocity at .

Determine the object’s velocity at .


A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m.

Calculate the magnitude of the shell’s acceleration.

For how much time is the shell accelerated?


A care package is dropped out of a cargo plane and lands in a forest. The impact with trees and snow bring the care package to rest from a downward vertical velocity of 54 m/s. The vertical distance the care package moves while in contact with trees and snow is 3.0 m. What is the package’s average acceleration while it moves this distance? Assume that downward displacement corresponds to positive values. Horizontal motion of the package is assumed to be negligible.


A swan on a lake gets airborne by flapping its wings and running on top of the water. The swan must reach a velocity of 5.25 m/s to take off, and accelerates from rest at an average rate of 0.44 m/s2.

How far will the swan travel before becoming airborne?

How much time will elapse between the swan starting to run and taking off?


During a slap shot, a hockey player accelerates the puck from a velocity of 6.88 m/s to 29.5 m/s without changing the direction that the puck is traveling. The shot takes place in s. What distance does the puck move through while it accelerates?


A motorcycle that is slowing down uniformly covers 2.0 successive km in 80 s and 120 s, respectively.

Calculate the acceleration of the motorcycle.

Calculate the velocity of the motorcycle at the end of the 2.0 km trip.

Calculate the velocity of the motorcycle at the beginning of the 2.0 km trip.


William is running in a straight line during a half-marathon, moving at a velocity of 4.2 m/s. Another runner, Liam, is 34 meters behind William, moving with the same velocity. Liam begins to accelerate in the direction of his velocity at 0.039 m/s2.

How long does it take Liam to catch William?

What distance does Liam travel while catching up with William?

What is Liam’s velocity when he catches up with William?


A cyclist in a race has a velocity of 10.2 m/s. The race leader has a velocity of 11.1 m/s. The cyclist is 2.35 m behind the race leader when the race leader is 246.5 m from the finish line, directly ahead. The cyclist begins to accelerate at a rate of 0.422 m/s2. She continues to accelerate until crossing the finish line, 6.29 s later.

What was the winning cyclist’s final velocity?

How much did the winning cyclist reduce their time by because of accelerating?

What was the difference in finish time between the winner and runner-up?

What was the distance between the runner-up and the winner when the winner crossed the finish line?


The position of a particle moving along the -axis varies with time according to .

Find the velocity of the particle at .

Find the acceleration of the particle at .

Find the time at which the position of the particle has a maximum value (not at ).

Find the time at which the velocity of the particle is zero.

Find the maximum value of .


A particle at rest leaves the origin with its velocity increasing with time according to . At 5.00 s, the particle’s velocity starts decreasing according to . This decrease continues until , after which the particle’s velocity remains constant at 7.00 m/s.

What is the position of the particle at ?

What is the position of the particle at ?

What is the position of the particle at ?


A car and a truck are travelling along a straight road at constant velocities of 78 km/h and 66 km/h respectively. The 8.4-m-long truck passes the 2.6-m-long car. How much time elapses between the moment the front of the truck is in line with the back of the car and the moment the back of the truck is in line with the front of the car?