Unit 1 : Kinematics in 1 – D
Problem Solving Strategy for Kinematics with Uniform Acceleration
1. Draw a picture. Define zero and positive space. Initial motion is positive is the easiest.
2. Make a list of variables. Read the question to insert information for the variables.
3. Eliminate equations with unknown variables.
Important: From rest (vo = 0 m/s), to a stop (v = 0 m/s), g = 10 m/s2
1. An object accelerates uniformly from 3.0 meters per second east to 8.0 meters per second east in 2.0
seconds.
(a) What is the magnitude of the acceleration of the object?
(b) How far did the object travel?
2. A passenger jet needs to reach a speed of 100 m/s on the runway for takeoff. The runway is 2500 m
long.
(a) What minimum average acceleration from rest is needed?
(b) How long is the plane acceleration before they take off?
3. A child riding a bicycle at 15 m/s accelerates at −3.0 m/s2 for 4.0 seconds.
(a) What is the child’s speed at the end of this 4.0-second interval?
(b) How far has the child traveled?
4. A car accelerates uniformly from rest to 15 m/s over a distance of 100 m.
(a) What the magnitude of the car’s acceleration?
(b) How much time passes during this motion?
Starting from rest, a jet takes 25 s and needs 1 500 m of runway to become airborne.
(a) What is its speed when it leaves the ground?
(b) What is the jet’s acceleration?
6. A car traveling on a straight road at 15.0 m/s accelerates uniformly to a speed of 21.0 m/s in 12.0
seconds.
(a) What is the distance traveled by the car?
(b) What is the car’s acceleration?
7. An inline skater is traveling a speed of 8.94 m/s. 120.0 s later she is climbing a hill at a speed of 7.15
m/s.
(a) What is her change in velocity?
(b) What is her average acceleration over the time frame?
(c) Assuming uniform acceleration, how far does she travel?
8. A sports car starting from rest can achieve 30.0 m/s in 4.7 s according to an advertisement in a
magazine.
(a) What is the average acceleration of the sports car?
(b) How far does the car travel?
9. A motorcycle accelerates uniformly from 12 m/s to 30 m/s while travelling 420 m.
(a) What is the motorcycle’s acceleration?
(b) How long did the acceleration take?
10. A car, initially traveling east with a speed of 5.0 meters per second, is accelerated uniformly at 2.0
m/s2 for 10 s along a straight line.
(a) How far does the car travel?
(b) What is the car’s final velocity?
11. A skier accelerates uniformly from 5.2 m/s to 12.8 m/s at 0.85 m/s2.
(a) What distance does the skier travel?
(b) How long does it take the skier to travel this distance?
12. An object starts at rest and accelerates at 4.0 m/s2. The object travels 48 m.
(a) How long did it take the object to travel this distance?
(b) What was the object’s final velocity?
13. Usain Bolt starts from rest and travels 100 meters in 9.2 s.
(a) Determine Usain’s acceleration. Assume uniform acceleration.
(b) Determine Usain’s final velocity when he crosses the finish line.
14. A dog is running 20.0 m/s when it sees a rabbit and accelerates at -8.0 m/s2 to a stop.
(a) How long did it take the dog to stop?
(b) How far did the dog travel?
15. The position function for the motion of a particle is given by x(t) = 20 – 12t + 4t2.
(a) What is the initial position?
(b) What is the initial velocity?
(c) What is the acceleration?
16. The velocity function for the motion of a particle is given by v(t) = 2.5t – 3.5.
(a) What is the initial velocity?
(b) What is the acceleration?