Question

Two objects $P$ and $Q$ , travelling in the same direction start from rest. While the object $P$ starts at time $t=0$ and object $Q$ starts later at $t=30min$ . The object $P$ has an acceleration of $40km/h^2$ . To catch $P$ at a distance of $20km$ , the acceleration of $Q$ should be

• A. $40km/h^2$
• B. $80km/h^2$
• C. $100km/h^2$
• D. $160km/h^2$

Answer 1

Answer: (D)

According to question,
Object $P$ starts at $t=0$ and acceleration of $P=40km/h^2$
The time taken by object $P$ to cover $20km$ will be,
$s=ut+\frac{1}{2}a{t}^2$
Where, $u=0,s=\frac{1}{2}a{t}^2$
$t=\sqrt{\frac{2s}{a}}$
Here, $a=40km/h^2$
and $s=20km$
$t=\sqrt{\frac{2\times 20}{40}}$
$=1hour$
Time taken by $Q$ will be $\frac{1}{2}hour$ , because it started after $30min$ .
The acceleration in $Q$ ,
$a=\frac{2s}{t^2}=\frac{2\times 20}{{\left(\frac{1}{2}\right)}^2}$
$=2\times 4\times 20$
$=160km/h^2$