Question

An empty truck moving on a straight road with a certain velocity can be stopped over a distance $s$ by applying the brakes. If the truck is loaded so that its mass now is one and half times that of the empty truck and is moving with the same velocity, it can be stopped by the brakes in a distance of (assume that the same braking force is acting in the two cases)

• A. $\frac{s}{2}$
• B. $2s$
• C. $\frac{3s}{2}$
• D. $\frac{2s}{3}$

Answer 1

Answer: (C)

$\frac{3s}{2}$

The use of break is to reduce the kinetic energy of a car using the frictional force between the tires of the car and the road. The empty car of mass m has a kinetic energy $=1/2\times m\times v^2$ and the work done by the frictional force (F) is = $F\times s$, where $s$ is the distance traveled by the truck before it can be stopped.

So, $1/2\times m\times v^2$= $F\times s$

or, $F=\frac{m\times v^2}{2\times s}$........................ (1)

Now when the truck is loaded then let the mass of it is M. And the distance traveled by the truck before it can be stopped is S.

$1/2\times M\times v^2$= $F\times S$ .............(2)

Using (1), we will get ,

$S=3/2\times s$.