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 V, the rate at which the engine of the car is doing work will be

Options

A. RV
B. maV
C. `(R+ma)V`
D. `(ma-R)V`

Explanation

To solve the problem, we need to determine the rate at which the engine of the car is doing work when the car is moving with a velocity \( V \), given that it has a mass \( m \), is accelerating at \( a \), and is experiencing a constant external resistive force \( R \).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Car:**
The car is subjected to two main forces:
- The resistive force \( R \) opposing the motion.
- The net force required to accelerate the car, which is \( F_{\text{net}} = ma \).

2. **Apply Newton's Second Law:**
According to Newton's second law, the net force acting on the car is equal to the mass of the car multiplied by its acceleration. Thus, we can express the total force \( F \) exerted by the engine as:
\[ F = ma + R \]
Here, \( ma \) is the force needed to accelerate the car, and \( R \) is the force needed to overcome the resistive force.

3. **Calculate the Power Output of the Engine:**
The power \( P \) delivered by the engine can be calculated using the formula:
\[ P = F \cdot V \]
Substituting the expression for \( F \) we derived earlier:
\[ P = (ma + R) \cdot V \]

4. **Final Expression for Power:**
Therefore, the rate at which the engine of the car is doing work when the velocity of the car is \( V \) is given by:
\[ P = (ma + R)V \]

### Conclusion:
The rate at which the engine of the car is doing work is \( P = (ma + R)V \).