Question

A car, moving at 1.5 $m{s}^{-1}$ applies brakes and comes to rest in $2s$. If the same car travels at double the speed, what time would it take to come to rest after applying brakes?

• A. $4s$
• B. $8s$
• C. $2s$
• D. $3s$

Answer 1

The correct option is A $4s$

Given,

Initial velocity $u_1=1.5m{s}^{-1}$
Final velocity $v_1=0$
Time taken $t_1=2s$

According to first equation of motion,
$v_1=u_1+a_1{t}_1$
$0=1.5+2a_1$
$a_1=\frac{-1.5}{2}=-0.75m{s}^{-2}$

Now, for the second case,

Initial velocity $u_2=3m{s}^{-1}$

Final velocity $v_2=0$

The braking system is still the same. So it provides the same retarding acceleration of $-0.75m{s}^{-1}$

So acceleration $a_2$ is same as $a_1=-0.75m{s}^{-1}$

Using first equation of motion again,
$v_2=u_2+a_1{t}_2$
$0=3-0.75\times t_2$
$t=\frac{3}{0.75}=4s$