# Worksheet: Kinematics

In this worksheet, we will practice using the SUVAT equations to calculate the change in displacement and velocity of an object undergoing constant acceleration.

**Q1: **

In 1,967, 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?

**Q2: **

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 1,000 m apart. Assuming both trains have the same acceleration, what must this acceleration be if the trains are to stop just short of colliding?

**Q6: **

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/s^{2}. 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?

**Q9: **

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.

**Q10: **

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/s^{2}.

How far will the swan travel before becoming airborne?

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

**Q12: **

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.

**Q13: **

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/s^{2}.

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?

**Q14: **

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/s^{2}. 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?

**Q15: **

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 .

**Q16: **

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 ?

**Q17: **

A car and a truck are traveling 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?

**Q18: **

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 1,000 s?

- A m
- B m
- C m
- D m
- E m

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

- A s
- B s
- C s
- D s
- E 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?

**Q19: **

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?

**Q21: **

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/s^{2} 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.

**Q24: **

A 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/s^{2} 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?