Answer to Question #257847 in Physics for Doodlebob

Question

car a has a headstart of 740 m ahead of car b car a is travelling at a constant 50km/h while car b starts from rest and accelerates at a constant 1.22m/s how long will it take car b to catch car a and how far will car b have traveled

Answer 1

Distance of car A relative to car B:

$$d=d_0+vt.$$

Distance of car B:

$$d=at^2/2.$$

Equate:

$$d_0+vt=at^2/2,\\\space\\ t^2\frac a2-tv-d_0=0,\\\space\\ t=48\text s.$$

The distance car B traveled:

$$d=at^2/2=1405\text m.$$