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

The correct option is (R+ma)v.

Step-by-step Explanation:

1. Identify the forces acting on the car:

Let the forward force exerted by the engine of the car be $F$.

The constant resistive force opposing the motion is given as $R$.

2. Apply Newton's Second Law of Motion:

The net force acting on the car in the direction of motion is the difference between the forward engine force and the resistive force:

$F_{\text{net}}=F-R$

According to Newton's second law, this net force is also equal to the product of the mass $m$ and the acceleration $a$ of the car:

$F_{\text{net}}=ma$

3. Calculate the engine force:

Equating the two expressions for the net force, we get:

$F-R=ma$

Solving for the engine force $F$:

$F=R+ma$

4. Find the rate of work done (Power):

The rate at which the engine does work is its power output, which is defined as the product of the engine force and the velocity $v$ of the car:

$P=F\cdot v$

Substituting the expression for $F$ into this formula, we get:

$P=(R+ma)v$

Thus, the rate at which the engine is doing work is $(R+ma)v$.