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Question

A particle moving in a straight line with initial velocity $$u$$ and uniform acceleration $$a$$. If the sum of the distance travelled in $${t}^{th}$$ and $${(t+1)}^{th}$$ seconds is $$100\ cm$$, then its velocity after $$t$$ seconds in $$cm/s$$ is 


A
20
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B
30
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C
50
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D
80
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Solution

The correct option is C $$50$$

Solution 2
Distance travelled is $$t^{th} sec =S(t)-S(t-1)$$
Distance travelled is $$(t+1)^{th} sec = S(t+1)-S(t)$$
$$S(t)-S(t-1)+S(t+1)-S(t)=100$$
$$S(t+1)=u(t+1)+\dfrac 12 a(t+1)^2$$
$$S(t-1)=u(t-1)+\dfrac 12 s(t-1)^2$$
$$S(t+1)+S(t-1)=$$
$$\Rightarrow 2(u+at)=100$$
$$u+at=50$$
1432408_1021952_ans_302033336b5a45649046351e0cbea381.PNG

Physics

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