This question is based on the application of derivatives (calculus).

A particle moves according to a law of motions=f(t) =t³-12t²+45t,t 0, where tis measured in seconds andsin feet (Positive velocity is movement to the right).

(a) Find the velocity at timet.

(b) When is the particle moving to the right?

(c) Is the particle speeding up or slowing down when t= 4sec.

(d) Find total distance travelled in the first 6 seconds.