Question

If a function s (t )gives the position of a function at time​ t, the derivative gives the​ velocity, that​ is, v (t )equalss prime (t ). For the given position​ function, find ​(a) v (t )and ​(b) the velocity when tequals​0, tequals5​, and tequals8.

Answer 1

a)
`s'(t) = v(t) = 38 t -10`

b)
`s'(t) = v(t) = 38 t -10`

We just need to replace the different values of t and see what we got:

t=0,
`v(0) = 38*0 -10 = -10`

t =5,
`v(5) = 38*5 -10 =180`

t=8,
`v(8)= 38*8 -10 = 294`

Explanation:

Assuming this complete 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=5​, and t=8.

"

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

Part a

The velocity is defined as
`v(t) =s'(t)`

And if we derivate the position we got:

`s'(t) = v(t) = 38 t -10`

Part b

Since we have the function for the velocity:

`s'(t) = v(t) = 38 t -10`

We just need to replace the different values of t and see what we got:

t=0,
`v(0) = 38*0 -10 = -10`

t =5,
`v(5) = 38*5 -10 =180`

t=8,
`v(8)= 38*8 -10 = 294`