A particle moves according to the law of motion with the function s(t)=(t^2)(e^-t) where S is measured in seconds and T is measured in feet

Question

s(t)=(t^2)(e^-t)

(a) Find the velocity at time t.

(b) What is the velocity after 3 seconds?

(c) When is the particle at rest?

(d) When is the particle moving in the positive direction?

Answer 1

a) Find v(t)= ds/dt

b) plug in t = 3 to expression in (a)

c) Find t when v(t) = 0

d) find t when v(t) > 0

s = t²e^-t ds/dt using product rule is (2t -t²)e^-t