A particle starts from a point O and moves in a straight line so that its displacement,

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A particle starts from a point O and moves in a straight line so that its displacement, s cm, from O at time t seconds is given by s = 2t sin πt/3.

a. Find expression for velocity, v, and the acceleration, a, of the particle at time t seconds.

b. Show that 18(vt – s) = t2(9a + π2s).

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