Question

An $1575kg$ 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. $10m{s}^{-1}$
• B. $15m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $25m{s}^{-1}$

Answer 1

The correct option is C $20m{s}^{-1}$

Since the car comes to a stop, its final velocity $v=0$. We need to find the initial velocity $u$.
Mass $=1575kg$
$d=45m$
Work done, $W=F\cdot d$
or, $W=7000\times -45$ (As force applied and displacement are in opposite directions)
$=-315000J$
We know,
$WorkDone,W=\Delta (K.E)$
$\Rightarrow -315000=(\frac{1}{2}\times m{v}^2)-(\frac{1}{2}\times m{u}^2)$
$\Rightarrow -315000=(0-(\frac{1}{2}\times 1575\times u^2)$
On solving we get $u=20m{s}^{-1}$.