Question

A van of mass $1200kg$ is travelling at a speed of $54km{h}^{-1}$. When brakes are applied it comes to rest in $10s$. Assume that all the mechanical energy converts to thermal energy during the braking mechanism. Find the average rate of production of thermal energy.

• A. $3327cal{s}^{-1}$
• B. $3237cal{s}^{-1}$
• C. $3227cal{s}^{-1}$
• D. $3290cal{s}^{-1}$

Answer 1

The correct option is C $3227cal{s}^{-1}$

Given,
Mass = $1200kg$
Speed $v=54km{h}^{-1}$
= $54\times \left(\frac{5}{18}\right)$ = $15m{s}^{-1}.$

$\therefore$ Total K.E = $\frac{1}{2}m{v}^2$

=$\frac{1}{2}\times 1200\times (15{)}^2$

= $135000J$

We know, $1cal=4.184J$

Total K.E = $\frac{135000}{4.184}=32265cal$

It is given that total mechanical energy is converted into thermal energy.

Thermal energy = $32265cal$.

Rate of production of thermal energy
= $\frac{32266}{10}=3226.6cal/s$

$\therefore$ The average thermal energy$\approx$ $3227cal{s}^{-1}$