Question

An $870kg$ car skids to a stop across a horizontal surface over a distance of $45m$. The frictional force acting on the car is $7000N$. What is the initial velocity of the car?

• A. $27.9m{s}^{-1}$
• B. $37.9m{s}^{-1}$
• C. $14m{s}^{-1}$
• D. $26.9m{s}^{-1}$

Answer 1

The correct option is D $26.9m{s}^{-1}$

Since the car comes to a stop, its final velocity $v=0$. We need to find the initial velocity $u$.
Mass $=870kg$
$d=45m$
Work done, $W=F\cdot d$
or, $W=7000\times -45$ (As force applied and displacement are in opposite directions)
$=-315000J$
We know,
$WorkDone,W=\Delta (K.E)$
$\Rightarrow -315000=(\frac{1}{2}\times m{v}^2)-(\frac{1}{2}\times m{u}^2)$
$\Rightarrow -315000=(0-(\frac{1}{2}\times 870\times u^2)$
On solving we get $u=26.9m{s}^{-1}$.