Question

You are standing at rest at a bus stop. A bus moving at a constant speed of 5.00 m/s passes you. When the rear of the bus is 14.0 m past you, you realize that it is your bus, so you start to run toward it with a constant acceleration of 0.960 m/s2.

Part A

How far would you have to run before you catch up with the rear of the bus?

Express your answer with the appropriate units.

Part B

How fast must you be running then? Find the final speed just as you reach the bus.

Express your answer with the appropriate units.

Answer 1

Let the time taken to catch the bus be t and the speed of the bus is 5 m/s.

The distance the bus covers in time t is 5 t and you have to travel an additional 14 m.

The total distance you have to travel is 14 + 5 t

The distance you traveled while accelerating is

Hence

where a = 0.96 m/s²

Therefore

Solving this quadratic equation gives 2 roots

You need to choose the positive root as the time is positive

Therefore the taken to reach the bus

A) The distance you have to run before you catch up with the rear of the bus is

B) Your speed when you reach the bus is