1.

The distance traversed by a moving particle at any instant is half of the product of its velocity and the time of travers. Show that the acceleration of particle is constant.

Answer» Let at an instant ` t, v` be the velocity of the moving praticle and (S) be the distance travelled by the
particle . As pre question.
` S =v t//2 ` …(i)
Defferntiating it w.r.t. time (t), we have
`(dS)/(dt) = 1/2 (d v)/(dt) xx t + v/2 `
or ` v =1/2 a xx t + v/2`
(:. (dv)/(dt) =acceleration =a)
or ` at =v`
Differntiating it again w..r.t. time (t), we have
` (da)/(dt) xx t + a = (d v)/(dt) =a or (da)/(dt) xx t=0`
or ` (da)/(dt) =0`.


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