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Question

A car moving on a road with uniform acceleration covers 20 m in the first second and 30 m in the next second.
What is its acceleration?

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A
20ms2
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B
10ms2
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C
30ms2
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D
5ms2
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Solution

The correct option is B $$10 m s^{-2}$$
Let the initial velocity be $$u$$ and acceleration be $$a$$.
Case 1 : 
Distance covered  $$S  = 20 \ m$$
Time taken  $$t = 1 \ s$$
Using   $$S = ut+\dfrac{1}{2}at^2$$
Or    $$20 = u(1)+\dfrac{1}{2}a(1)^2$$
$$\implies \ 20 =u+\dfrac{a}{2}$$
We get   $$u = 20-\dfrac{a}{2}$$
Case 2 :
Total distance covered   $$S = 20+30 = 50 \ m$$
Total time taken   $$t = 1+1 = 2  s$$
So,   $$50 = u(2)+\dfrac{1}{2}a(2)^2$$
or   $$50 = 2u +2a$$
Or   $$50 = 2(20-\dfrac{a}{2}) + 2a$$
Or   $$50 = 40-a+2a$$
$$\implies \ a = 10 \ m/s^2$$

Physics

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