Question

How long will it take a car starting from rest to travel 659.0 km if its acceleration is 2.4 m/s/s?

Answer 1

Task. How long will it take a car starting from rest to travel $d=659.0$ km if its acceleration is $a=2.4\ m/s^{2}$?

Solution. The formula for the distance by time $t$ passed with constant acceleration has the following form:

$d(t)=v_{0}t+\frac{at^{2}}{2}.$

In our case the initial velocity $v_{0}=0$, so

$d(t)=\frac{at^{2}}{2},$

whence

$t=\sqrt{\frac{2d}{a}}.$

We should find $t$ such that $d=659\ km\ =659000\ m$ and acceleration is $a=2.4\ m/s^{2}$. Substituting values we get:

$t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2*659000}{2.4}}=741.06\ sek=\frac{741.06}{60}min=12.35\ min.$