Question

A particle moves according to a law of motion s = f(t), 0 ≤ t ≤ 12, where t is measured in seconds and s in feet.
f(t) = cos(πt/6)

(a) Find the velocity at time t (in ft/s).

b.) What is the velocity after 5 s? (Round your answer to two decimal places.)

c.) When is the particle at rest? (there are supposed to be three answers for this part)

d.) When is the particle moving in the positive direction? (Enter your answer using interval notation.)


E.) Find the total distance traveled during the first 12 seconds.

F.) Find the acceleration at time t (in ft/s2).

Answer 1

a) v= f'(t), so, take derivative of f
b) replace value t =5 into the equation of v above to find v at t =5
c) when it is at rest v =0, plug it into the equation of v (part a) to find t. that t is when it is at rest

Answer 2

d) solve for f(t) >0
e) replace t =0 and t = 12 into f to find f(0) and f(12) , subtract them , OR take integral of v , limit from 0 to 12
f)accelerate =v' , take derivative of v ,

Answer 3

can anyone elaborate a little more on parts c,d, and e ?