The displacement of an object in motion is described by s(t) = t^3 -21t^2+ 90t, where the horizontal displacement, s, is measured in metres at t seconds.

a) Calculate the displacement at 3 s.

b) Calculate the velocity at 5 s.

c) Calculate the acceleration at 4s.

The forward motion of a space shuttle, t seconds after touchdown, is described by s(t) = 189t - t^{\frac{7}{3}}, where s is measured in metres.

a. What is the velocity of the shuttle at touchdown?

b. How much time is required for the shuttle to stop completely?

c. How far does the shuttle travel from touch down to a complete stop?

d. What is the deceleration 8 s after touch down?