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

Answer:

a = 14 m/min²

Step-by-step explanation:

The displacement of bike is given by :

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

Velocity, $v=\dfrac{ds(t)}{dt}$

Finding velocity of the bike.

$v=\dfrac{d}{dt}(t^3-2t^2+3)\\\\=3t^2-4t$

Acceleration, $a=\dfrac{dv(t)}{dt}$

$a=\dfrac{d}{dt}(3t^2-4t)\\\\=6t-4$

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.