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 tequals0, tequals5, and tequals8.

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.

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[tex] s(t) = 19t^2 -10 t + 5[/tex]

Part a

The velocity is defined as [tex] v(t) =s'(t)[/tex]

And if we derivate the position we got:

[tex] s'(t) = v(t) = 38 t -10 [/tex]

Part b

Since we have the function for the velocity:

[tex] s'(t) = v(t) = 38 t -10 [/tex]

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

t=0, [tex] v(0) = 38*0 -10 = -10[/tex]

t =5, [tex] v(5) = 38*5 -10 =180[/tex]

t=8, [tex] v(8)= 38*8 -10 = 294[/tex]

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.

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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 tequals0, tequals5, and tequals8.