The engine of a car produces an acceleration of `6ms^(-2)` in the car. If this car pulls another car of the same mass, then the acceleration would be

Options

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

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the initial scenario
The car produces an acceleration of \(6 \, \text{m/s}^2\) when it is moving alone. Let's denote the mass of the car as \(m\).

### Step 2: Calculate the force exerted by the engine
Using Newton's second law of motion, we know that:
\[ F = m \cdot a \]
Here, the acceleration \(a = 6 \, \text{m/s}^2\). Therefore, the force \(F\) exerted by the engine is:
\[ F = m \cdot 6 = 6m \]

### Step 3: Consider the new scenario with two cars
Now, the car is pulling another car of the same mass \(m\). The total mass being pulled is:
\[ \text{Total mass} = m + m = 2m \]

### Step 4: Apply Newton's second law to the new scenario
The same force \(F = 6m\) is now acting on the total mass of \(2m\). We can set up the equation:
\[ F = \text{Total mass} \cdot \text{New acceleration} \]
Substituting the values we have:
\[ 6m = 2m \cdot a_{\text{new}} \]

### Step 5: Solve for the new acceleration
To find the new acceleration \(a_{\text{new}}\), we can simplify the equation:
\[ 6m = 2m \cdot a_{\text{new}} \]
Dividing both sides by \(2m\) (assuming \(m \neq 0\)):
\[ a_{\text{new}} = \frac{6m}{2m} = 3 \, \text{m/s}^2 \]

### Conclusion
The new acceleration of the car when it pulls another car of the same mass is:
\[ \boxed{3 \, \text{m/s}^2} \]

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