Question

A car enters the freeway with a speed of 5.6 m/s and accelerates uniformly for 3.7 km in 4.2 minutes. How fast is the car moving after this time? Answer reported in m/s.

Answer 1

4.2 minutes = 4.2 · 60 seconds = 252 seconds. 3.7 km = 3700 m.

Equation for displacement is

$S=v_{0}\cdot t+at^{2}/2$

Equation for velocity

$v=v_{0}+at$

From these we can find

$a=\frac{2(S-v_{0}t)}{t^{2}}=\frac{2(3700-5.6\cdot 252)}{252^{2}}=0.072\,m/s^{2}$

$v=5.6+0.072\cdot 252\approx 23.7\,m/s$

Final velocity is 23.7 m/s.