Two objects, X and Y, accelerate from rest with the same constant acceleration.

Question

Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for twice the time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration? 8. (A) Object X is moving at the same speed as object Y. B) Object X is moving four times faster than object Y. C Object X has traveled the same distance as object Y. Object X has traveled twice as far as object Y. E Object X has traveled four times as far as object Y.

Explanation / Answer

v = u + at

s = ut + 1/2*a*t^2

and since they start from 0 => u = 0

=> v = at and s = 1/2*a*t^2

final displacement is dependent upon square of time for which the acceleration is applied

and final velocity is linearly dependent upon time for which the accelefation is applied

=> object X will move with velocity two times the object Y and object X has travelled four times more than object Y

hence option(E) is correct

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