Question

Two object, $P$ and $Q$, travelling in the same direction starts from rest. While the object $P$ starts at time $t=0$ and object $Q$ starts later at $t=30$ min. 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. $120km/h^2$
• E. $160km/h^2$

Answer 1

Answer: (E)

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,
$s=u+\frac{1}{2}a{t}^2$
Where, $u=0,s=\frac{1}{2}a{t}^2$
$t=\sqrt{\frac{2s}{a}}$
Here, $a=40km/h^2$
and $s=20kn$
$t=\sqrt{\frac{2\times 20}{40}}$
$=1$ hour
Time taken by $Q$ will be $\frac{1}{2}$ hour, because he
started after $30$ min.
The acceleration in $Q$,
$a=\frac{2s}{t^2}=\frac{2\times 20}{{\left(\frac{1}{2}\right)}^2}$
$=2\times 4\times 20$
$=160km/h^2$