stuck on an average velocity question

Question

The position of an object moving along a line is given by the function s left parenthesis t right parenthesis equals negative 19 t squared plus 57 ts(t)=−19t2+57t. Find the average velocity of the object over the following intervals.

(a) [1, 66]
(b) [1, 55]
(c) [1, 44]
(d) [1, 1+h] where hgreater than>0 is any real number.

 

i need help with (d)

Answer 1

 

Over a time interval [t₁, t₂], the average speed <v> is given by

 

<v> = [s(t₂) - s(t₁)] / (t₂ - t₁)

 

You are given

 

s(t) = -19t² + 57t

 

and several time intervals [t₁, t₂].  Just plug in the time values of the ends of the time intervals and compute the average speed using the formula above for <v>.  These are all worked the same. In problem (d), you will end up with an average speed as a function of h.