Find a function for the velocity.

Question

Let s(t) = 4t³ +12t² -180t be the equation of motion for a particle. Find a function for the velocity.

v(t)

Where does the velocity equal zero? [Hint: factor out the GCF.]

t =

and t =

Find a function for the acceleration of the particle.

a(t)

Answer 1

Given

s(t) = 4t³ + 12t² – 180t

v(t)

since v(t) = ds/dt we get

v(t) = 12t² + 24t – 180

When v(t) = 0

v(t) = 0 = 12t² + 24t – 180 = 12(t² + 2t – 15)

So t² + 2t – 15 = (t + 5)(t – 3) = 0

t + 5 = 0 gives t = –5

t – 3 = 0 gives t = 3

Since t can't be negative (no time travel allowed!), our answer is

t = 3

a(t)

Since a(t) = dv/dt we get

a(t) = 24t + 24

Answers

velocity equals zero when t = 3

a(t) = 24t + 24