Question

A car's engine accelerates the vehicle at a rate of $6{\mathrm{ms}}^{-2}$.If this car pulls another car of the same mass, then the acceleration would be

• A. $6{\mathrm{ms}}^{-2}$
• B. $12{\mathrm{ms}}^{-2}$
• C. $3{\mathrm{ms}}^{-2}$
• D. $1.5{\mathrm{ms}}^{-2}$

Answer 1

The correct option is C

$3{\mathrm{ms}}^{-2}$

Step 1: Given data:

The acceleration of the car $a=6{\mathrm{ms}}^{-2}$

Step 2: Formula used:

Newton's second law-

$F=ma$

Where $m,a$ are mass of the body and acceleration respectively.

Step 3: Calculating the acceleration:

Let $M$be the car's mass.

From Newton's second law of motion, it can be concluded that the maximum force applied by the engine is,

$F=Ma$

Putting the known value, the maximum force applied by an engine,

$F=6M$

Now since the same engine is applying force for pulling the another car of same mass

This time the total mass pulled by an engine will be,

$M+M=2M$.

Since maximum force applied by an engine is-

$6M$

Let the acceleration would be $a\text{'}$

Then according to newton's second law-

$\begin{array}{rcl}2M\times a& =& 6M\\ 2M\times a& =& 6M\\ 2a& =& 6\\ a& =& 3m/s^2\end{array}$

Thus the acceleration will be $3{\mathrm{ms}}^{-2}$.

Hence, option C is the correct answer.