Question

Two object P and Q, traveling in the same direction starts 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. $120km/h^2$
• E. $160km/h^2$

Answer 1

Answer: (E)

$160km/h^2$

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, $a=40$ $km/h^2$

and $s=20$km

$t=\sqrt{\frac{2\times 20}{40}}$

$=1$ hour

Time taken by Q will be $\frac{1}{2}$ hour, because he started after $30$min.

The acceleration of Q,

$a=\frac{2s}{t^2}=\frac{2\times 20}{{\left(\frac{1}{2}\right)}^2}$

$=2\times 4\times 20$

$=160km/h^2$.