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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
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B
80km/h2
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C
100km/h2
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D
120km/h2
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E
160km/h2
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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
$$t=\sqrt{\dfrac{2\times 20}{40}}$$
$$=1$$ hour
Time 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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