The engine of a car produces acceleration 4m/sec² in the car, if this car pulls another car of same mass, what will be the acceleration produced

The correct answer is 2 m/s².

Let us break down the solution step-by-step using Newton's second law of motion.

Step 1: Understand Newton's Second Law
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
$F=m\cdot a$
where:
- $F$ is the force produced by the engine,
- $m$ is the mass of the car, and
- $a$ is the acceleration produced.

Step 2: Define the initial scenario
In the first case, the engine produces an acceleration of $4{\text{m/s}}^2$ on a single car of mass $m$. Therefore, the force $F$ produced by the engine is:
$F=m\cdot 4$

Step 3: Analyze the second scenario
When this car pulls another car of the same mass $m$, the total mass being accelerated by the same engine force $F$ doubles. Let the new total mass be $m^{\prime }$:
$m^{\prime }=m+m=2m$

Step 4: Calculate the new acceleration
Let $a^{\prime }$ be the new acceleration produced. Using Newton's second law for the combined system:
$F=m^{\prime }\cdot a^{\prime }$
Substitute the values we know into this equation:
$m\cdot 4=2m\cdot a^{\prime }$
Divide both sides by $m$ (assuming mass $m\ne 0$):
$4=2\cdot a^{\prime }$
Solving for $a^{\prime }$ gives:
$a^{\prime }=\frac{4}{2}=2{\text{m/s}}^2$

Thus, the acceleration produced when pulling another car of the same mass is $2{\text{m/s}}^2$.