Question

Amy purchased a brand–new mountain bike, which she's riding through the winding trails. The bike's displacement is given by

s(t) = t3 − 2t2 + 3. What is the bike's acceleration after three minutes?

Answer 1

a = 14 m/min²

Explanation:

The displacement of bike is given by :

`s(t)=t^3-2t^2+3`

Velocity,
`v=(ds(t))/(dt)`

Finding velocity of the bike.

`v=(d)/(dt)(t^3-2t^2+3)\\\\=3t^2-4t`

Acceleration,
`a=(dv(t))/(dt)`

`a=(d)/(dt)(3t^2-4t)\\\\=6t-4`

At t = 3 minutes,

a = 6(3) - 4

= 18-4

= 14 m/min²

So, the bike's acceleration after 3 minutes is 14 m/min².