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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 1 0 0 0 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 minutes of travel?

What distance does the cyclist travel?


An object has an acceleration of 1.2 cm/s2. At 𝑡 = 4 . 0 s , its velocity is 3 . 4 cm/s.

Determine the object’s velocity at 𝑡 = 1 . 0 s .

Determine the object’s velocity at 𝑡 = 6 . 0 s .


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 1 . 3 2 × 1 0 2 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 𝑥 -axis varies with time according to 𝑥 ( 𝑡 ) = 5 . 0 𝑡 4 . 0 𝑡 2 3 m .

Find the velocity of the particle at 𝑡 = 2 . 0 s .

Find the acceleration of the particle at 𝑡 = 2 . 0 s .

Find the time at which the position of the particle has a maximum value (not at 𝑡 = 0 ).

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

Find the maximum value of 𝑥 .


A particle at rest leaves the origin with its velocity increasing with time according to 𝑣 ( 𝑡 ) = 3 . 2 0 𝑡 / m s . At 5.00 s, the particle’s velocity starts decreasing according to 𝑣 = 1 6 . 0 1 . 5 0 ( 𝑡 5 . 0 0 ) / m s . This decrease continues until 𝑡 = 1 1 . 0 s , after which the particle’s velocity remains constant at 7.00 m/s.

What is the position of the particle at 𝑡 = 5 . 0 0 s ?

What is the position of the particle at 𝑡 = 7 . 0 0 s ?

What is the position of the particle at 𝑡 = 1 2 . 0 s ?


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?


Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object

How far away is the planet Venus if the echo time is 1 0 0 0 s?

  • A 1 . 4 3 × 1 0 1 1 m
  • B 1 . 3 8 × 1 0 1 1 m
  • C 1 . 5 5 × 1 0 1 1 m
  • D 1 . 5 0 × 1 0 1 1 m
  • E 1 . 6 0 × 1 0 1 1 m

What is the echo time for a car 75.0 m from a highway police radar unit?

  • A 5 . 0 0 × 1 0 7 s
  • B 5 . 1 5 × 1 0 7 s
  • C 5 . 0 7 × 1 0 7 s
  • D 4 . 9 1 × 1 0 7 s
  • E 5 . 2 0 × 1 0 7 s

How small a time interval must be measurable to use echo timing to find the distance to an aircraft to a precision of 10.0 meters?


You are driving your car on a straight road that has a coefficient of friction between the tires and the road of 0.50. A large piece of debris falls in front of your view and you immediately apply your car’s brakes. Coming to rest, your car leaves a straight, 28-m-length skid mark behind it. What speed were you driving at before applying the brakes?


The position of a particle moving along the 𝑥 -axis is given by 𝑥 ( 𝑡 ) = 4 . 0 2 . 0 𝑡 m.

At what time does the particle cross the origin?

What is the displacement of the particle between 𝑡 = 3 . 0 s and 𝑡 = 6 . 0 s .


A police car waits in hiding slightly off a highway. A speeding car passes the police car, moving at 40 m/s. At the instant the speeding car passes the police car, the police car accelerates from rest at 4.0 m/s2 to catch the speeding car. How long does it take the police car to draw level with speeding car? Ignore any motion that the police car would need to make in any direction other than the direction of the speeding car’s motion.


A ball is thrown and then caught in a padded mitt. It takes 2.66 ms from the time the ball first touches the mitt for the ball to stop. The horizontal deceleration of the ball provided by the mitt is 1 . 2 9 × 1 0 4 m/s2. Ignoring vertical motion, calculate the initial velocity of the ball?


A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle, catching up after 30 s of acceleration. What is the magnitude of the acceleration of the person?


A 1 . 3 0 × 1 0 - m - l o n g 2 express train passes through a station with a platform that is 255 m long. The train enters the station with an initial velocity of 34.2 m/s and decelerates at a rate of 0.185 m/s2 while it passes through.

How fast is the train moving when the front end of the train leaves the station?

For how much time is the front end of the train within the station?

What is the velocity of the train as the rear end of the train leaves the station?

How much time passes between the front end of the train entering the station and the rear end of the train leaving the station?


A dragster has an acceleration of 26.0 m/s2. Starting from rest, the dragster accelerates at this rate for 5.56 s. What distance does the dragster move in this time?


In a 100-m race, the winner is timed at 10.7 s. The second-place finisher’s time is 11.0 s. If the velocity of each runner is constant throughout the race, how far is the second-place finisher behind the winner when the winner crosses the finish line?