The engine of a car produces acceleration `4m//s^(2)` in the car. If this car pulls another car of same mass, what will be the acceleration produced

Options

A. `6 ms^(-2)`
B. `12 ms^(-2)`
C. `3 ms^(-2)`
D. `1.5 ms^(-2)`

Answer

To solve the problem step by step, we will analyze the forces acting on the cars and apply Newton's second law of motion.

### Step 1: Understand the given information
The engine of the car produces an acceleration of \(4 \, \text{m/s}^2\) when it is not pulling any other car. Let's denote the mass of the car as \(M\).

### Step 2: Calculate the force produced by the engine
Using Newton's second law, the force \(F\) exerted by the engine can be calculated as:
\[ F = M \cdot a \]
where \(a = 4 \, \text{m/s}^2\). Therefore, the force is:
\[ F = M \cdot 4 = 4M \]

### Step 3: Analyze the situation when the car pulls another car
When the first car pulls another car of the same mass \(M\), the total mass being accelerated is now \(M + M = 2M\).

### Step 4: Set up the equation for the new acceleration
Using the same force \(F = 4M\) and applying it to the total mass \(2M\), we can set up the equation:
\[ F = (2M) \cdot a' \]
where \(a'\) is the new acceleration. Substituting the force we found:
\[ 4M = (2M) \cdot a' \]

### Step 5: Solve for the new acceleration
To find \(a'\), we can divide both sides of the equation by \(2M\):
\[ a' = \frac{4M}{2M} = 2 \, \text{m/s}^2 \]

### Conclusion
The acceleration produced when the first car pulls another car of the same mass is \(2 \, \text{m/s}^2\).

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