Question

A pedestrian is running at his maximum speed of 6.0 m/sec to catch a bus stopped at a traffic light. When his is 15m from the bus, the light changes and the bus accelerates uniformly at 1m/s/s. Does he make it to the bus? If so , how far does he have to run in order to catch it? If not, how close does he get?

Answer 1

The position of pedestrian is described by:

$$x_p=v_0t=6t$$

The position of the bus:

$$x_b=15+\frac{at^2}{2}=15+0.5t^2$$

At the moment when they meet:

$$x_p=x_b$$

$$6t=0.5t^2+15$$

The smallest positive solution of this equation is:

$$t=3.55s$$

So, at t=3.55s, the pedestrian catches the bus.

The distance is:

$$S=v_0t=6*3.55= 21.3 m$$