Question

A car of mass $1000$ $kg$ moving with a velocity of $10m{s}^{-1}$ is acted upon by a forward force of $1000$ $N$ due to engine and retarding force of $500$ $N$ due to friction. It's velocity after $10$ $s$ is

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

Answer 1

The correct option is B $15$ $m{s}^{-1}$

For a body in equilibrium,
Equating forces along Y-axis,
Normal reaction $N=mg$
Equating forces along X-axis,
$ma+\mu N=F$
$ma+\mu mg=F$
$ma=F-\mu mg$
$a=\frac{F-\mu mg}{m}$
$a=\frac{1000-500}{1000}$
$\therefore a=0.5m/s^2$

Now,
$v=u+at$
$\therefore v=u+a\times t$
$\therefore v=10+0.5\times 10$
$\therefore v=15m/s$