1.The position of a moving particle as a function of time is given by

s(t) = 1/3t^3 – t +1, where s is in meters and t is in seconds. Find the time at which the particle is at rest and the acceleration of the particle at t = 3 s.

2. A car moves on a straight road. The cars position at time t is given by s(t) =

t+ sin t where s is in meters and t in seconds. Find the acceleration at t = Pi/4;s.

3. Find d /dx [ 1 + sin^2 x / x tan^315x]

4. df^-1 /dx for f(x) = x + 3 / 2x + 5

at x = 3