A particle is moving along a striaght line so that t its displacement s from a fixed point on the line is given s=a sin (bt+c) where a,b,c are cosntants. If v and f are the velocity and the acceleration of the particle respectively at time t, prove that `(i)v^(2)-fs ` is a constant (ii) `(df)/(ds)` is a constant and (ii) `s, (df)/(ds)=f`.

Answer

`-b^(2)s `