195k views
5 votes
The distance (miles) a rider travels on a mountain trail is given by s(t) = 3t^3 + 2t^2 + 4. What is the rider's acceleration after two minutes?

A.

36 miles/min2

B.

38 miles/min2

C.

40 miles/min2

D.

44 miles/min2

User Arnuschky
by
6.4k points

1 Answer

2 votes

Answer:

To determine the rider's acceleration after two minutes, we need to find the second derivative of the distance function s(t) = 3t^3 + 2t^2 + 4 with respect to time. In other words, we need to find the rate of change of the rider's velocity.

The first derivative of s(t) with respect to time is v(t) = 9t^2 + 4t.

The second derivative of s(t) with respect to time is a(t) = 18t + 4.

Now that we have the second derivative, we can find the acceleration after two minutes.

a(2) = 18(2) + 4 = 40 miles/min^2

Therefore the rider's acceleration after two minutes is C. 40 miles/min^2

User Xzibit
by
7.2k points