Answer to Question #233806 in Physics for Sean

Question

A student is running at a constant velocity of 5 m/s in an effort to catch a bus parked at a station. When he is 10 m away from the bus, the bus pulls away with constant acceleration of 1.2 m/s2. How much time will it take the student to catch the bus if he keeps running with the same velocity?

Answer 1

Given:

$v=5\:\rm m/s$

$a=1.2\:\rm m/s^2$

$l=10\:\rm m$

The distance traveled by a student

$$d_s=vt$$

The distance traveled by a bus

$$d_b=at^2/2$$

We get

$$d_s+l=d_b$$

$$vt+l=at^2/2$$

$$5t+10=0.6t^2$$

$$0.6t^2-5t-10=0$$

Root

$$t=3.3\:\rm s$$