Question

A car is moving with an initial velocity of $10{\text{m s}}^{-1}$ and an acceleration of $5{\text{m s}}^{-2}$ for a time interval of $10\text{s}$. If the mass of the car is $20\text{kg}$, find the average power of the car.

• A. 3500 W
• B. 7000 W
• C. 2000 W
• D. 5000 W

Answer 1

The correct option is A

3500 W

Mass of the car, $m=20\text{kg}$
The initial velocity of the car, $u=10{\text{m s}}^{-1}$
acceleration of the car, $a=$ $5{\text{m s}}^{-2}$
Time interval, $t=10\text{s}$
Let final velocity after time $t$ be $v$
We know that,$v=u+at$ (from equation of motion).
$v=10+5$$\times$ $10$ $=60{\text{m s}}^{-1}$

Work done = Change in kinetic energy = $\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$=\frac{1}{2}$ $\times$ $20(3600-100)=35000\text{J}$

$\text{Power}=\frac{\text{Work done}}{\text{time taken}}=$
$\frac{35000}{10}=3500\text{W}$