Question

You are running to catch a bus which has just started to move away from the stop. You are on a flat, straight road and you and the bus both start from zero velocity at time t = 0 s. Draw a velocity vs time and a position vs time to reinforce your answer Given the data below:

Object	Acceleration	Stamina
Human	0-30km/hr in 5 seconds	Can go at top speed for 10 seconds
Bus	0-50km/hr in 15 seconds	Can go at top speed for a long time

a) How far can you run before you get exhausted?

b) How far has the bus moved in the meantime?

c) Based on your answers in the first 2 parts, what is the maximum distance you can be behind the bus to catch up with it?

Answer 1

a) How far can you run before you get exhausted:

We can run at maximum speed for 10 seconds. To reach maximum speed, we took 5 seconds, thus in total we ran for 15 seconds.

Maximum speed,

With this maximum speed, we covered a distance of 8.33*10 = 83.3 m

Now, in first 5 seconds, we covered 's' distance where,

Thus, we can run 20.825 + 83.3 meters = 104.125 meters.

b) How far has the bus moved in the meantime:

We ran for 15 seconds, in this time the bus reached its maximum speed. Distance moved by bus is

(v = 50 km/h = 13.89 m/s)

c) Based on your answers in the first 2 parts, what is the maximum distance you can be behind the bus to catch up with it:

The maximum distance we can be behind the bus is