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/h2
B
80km/h2
C
100km/h2
D
120km/h2
E
160km/h2

Solution

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

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