Question

a train travels along a horizontal line according to the function s(t)=8t3 3t2 2t 4 where t is measured in hours and s is measured in miles. what is the velocity function v(t)?

Answer 1

The velocity function v(t) is
`24t^2 - 6t - 2`

To find the velocity function v(t), you need to take the derivative of the position function s(t) with respect to time t. The velocity is the rate of change of position with respect to time.

Given the position function s(t) =
`8t^3 - 3t^2 - 2t + 4`, let's find v(t):

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

Taking the derivative of s(t) with respect to t, you get:

v(t) =
`(d)/(dt)(8t^3 - 3t^2 - 2t + 4)`

v(t) =
`24t^2 - 6t - 2`

So, the velocity function v(t) is
`24t^2 - 6t - 2`