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
B
30
C
50
D
80

Solution

The correct option is C $$50$$Solution 2Distance travelled is $$t^{th} sec =S(t)-S(t-1)$$Distance travelled is $$(t+1)^{th} sec = S(t+1)-S(t)$$$$S(t)-S(t-1)+S(t+1)-S(t)=100$$$$S(t+1)=u(t+1)+\dfrac 12 a(t+1)^2$$$$S(t-1)=u(t-1)+\dfrac 12 s(t-1)^2$$$$S(t+1)+S(t-1)=$$$$\Rightarrow 2(u+at)=100$$$$u+at=50$$Physics

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