Question

If a function s(t) gives the position of a function at time t, the derivative gives the velocity, that is, v(t) = s'(t). For the given position function, find (a) v(t) and (b) the velocity when t = 0, t = 2, and t = 9.

s(t) = 19 t^2 - 10t + 5
v(t) =________.

Answer 1

(a)v(t)=38t-10

(b)

• v(0)=-10
• v(2)=66
• v(9)=332

Explanation:

Given the position of a function, s(t) at time t as:

`s(t) = 19 t^2 - 10t + 5`

(a)Velocity, v(t)

`If \:s(t) = 19 t^2 - 10t + 5\\`

Then:

s'(t)=38t-10

The velocity, v(t) of the function at time (t) is:

v(t)=38t-10

(b)If v(t)=38t-10

At t=0, v(0)=38(0)-10=-10

At t=2, v(2)=38(2)-10=66

At t=9, v(9)=38(9)-10=332

We are not given units, but velocity is always a function of distance per time.