Question

A car of mass $m$ is driven with acceleration $a$ along a straight level road against a constant external resistive force $R$. When the velocity of the car is $V$, the rate at which the engine of the car is doing work will be________

Answer 1

Step 1: Given

Mass of the car: $m$

Acceleration: $a$

External resistive force: $R$

Velocity: $V$

Step 2: Formula used

Power is given by, $P=Force\times velocity$

Step 3: Determine the total force

F is the net force acting on the body.

Reactive force (R) is acting in the same direction as the acceleration (a) as the resistive force is against the net force.

The sum of all the forces acting on the car is,

$F=R+ma$

Step 4: Determine the power

Power is given by,

$$\begin{gathered} P=Force\times velocity \\ =(R+ma)V \end{gathered}$$

Therefore, the rate at which the engine of the car is doing work will be $(R+ma)V$.