A particle is moving in a straight line with initial velocity u and uniform acceleration f. if the sum of the distances travelled in t and t+1 seconds is 100 cm, then its velocity after t seconds in cm/s is ?

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Answer 1 · 2017-08-02T11:59:47

The velocity is $= (100 - \frac{1}{2} f) c m s^{- 1}$ $=(100-1/2f) cms^-1$

We apply the equation of motion

$s = v t + \frac{1}{2} a t^{2}$ $s=vt+1/2at^2$

$Deltas=vDeltat+1/2a(Deltat)^2$

The velocity after $ts$ is $=vcms^-1$

$Deltat=t+1-t=1s$

The acceleration is $a=f cms^-2$

The distance is $Deltas=100cm$

Therefore,

$100=(vxx1)+(1/2xxfxx1)$

$v=(100-1/2f) cms^-1$