Question

A car $A$ is travelling on a straight level road with a uniform speed of $60km/h$. It is followed by another car $B$ which is moving with a speed of $70km/h$. When the distance between them is $2.5km$, the car $B$ is given a deceleration of $20\frac{km}{h^2}$. After how much time will $B$ catch up with $A$?

• A. $1/4hr$
• B. $1/2hr$
• C. $1hr$
• D. $1/8hr$

Answer 1

The correct option is B $1/2hr$

Step: 1 Find the distance covered by $A$.
Distance covered by car $A$ in time $t$ is, $s_1=60t$

Step: 2 Find the distance covered by $B$.
$s=$distance covered $=s_2$

$u=$ initial velocity $=70km/h$

$a=$ acceleration $=-20\frac{km}{h^2}$

$t=$ time $=t$

From second equation of motion:
$s=ut+\frac{1}{2}a{t}^2$

$s_2=70t+\frac{1}{2}(-20)\times t^2$

$s_2=70t-10t^2$

Step: 3 Find the time when $B$ will catch $A$.
But it is given that
$s_2-s_1=2.5km$

$70t-10t^2-60t=2.5$

$10t-10t^2=2.5$

$t-t^2=0.25$

$t-t^2-0.25=0$

$t^2-t+0.25=0$

$(t-0.5{)}^2=0$

$t=0.5hr$