v(t)=0.01t^4 - 0.04t^3 t>or equal to 0 where t is time (seconds) and v is velocity (ft/s)
a) Find velocity at time t.
b) What is velocity after 3 s?
c) When is the particle at rest?
d) When is the particle moving in the positive direction?
e) Find the total distance traveled in the first 8 s.
f) Draw diagram to illustrate the motion of the particle.
g) Find the acceleration at time t and after 3 s.
h) Graph the position, velocity, and acceleration functions for 0 <or equal t <or equal 8
i) When is the particle speeding up? When is it slowing down?
Please explain step by step along with the answer, thank you.