Question

The driver of a speeding empty truck slams on the brakes and slows down to a stop through a distance d. On a second trial, the truck carries a load that doubles its mass. What distance will the loaded truck cover to come to rest, when it is moving at the same speed and the brakes are slammed?

Answer 1

Empty truck:

$d=\frac{v^2}{2a}$

$F=ma=m\frac{v^2}{2d}$

The truck with load ($m'=3m)$ :

$d'=\frac{v'^2}{2a'}$

$F'=3ma'=3m\frac{v^2}{2d'}$

Then $F=F'$

$m\frac{v^2}{2d}=3m\frac{v^2}{2d'}$

$\frac{3}{d'}=\frac{1}{d}$ where $d'=3d$