The position of an object moving vertically along a line is given by the function s(t) = -16t^2 + 128t. find the average velocity of the object over the following intervals.

a. [1, 4]
b. [1, 3]
c. [1, 2]
d. [1, 1 + h], where h > 0 is a real number

a) 48

b) 64

c) 80

d) 96-16h

Step-by-step explanation:

a) s(1)=112 and s(4)=256

average velocity on [1,4] = (256-112)/(4-1) = 48

b) s(1)=112 and s(3)=240

average velocity on [1,3] = (240-112)/(3-1) = 64

c) s(1)=112 and s(2)=192

average velocity on [1,2] = (192-112)/(2-1) = 80

the next one's tricky to type. watch the parentheses carefully:

d) s(1)=112 and s(1+h)= -16(1+h)^2 + 128(1+h)

average velocity on [1,1+h] =

(s(1+h) - s(1))/((1+h)-1) = (-16(1+h)^2 +128(1+h) - (112))/h

= (-16(1+2h+h^2)+128+128h - 112)/h

= ( -16 -32h -16h^2 + 16 + 128h)/h

= ( 96h - 16 h^2)/h

= 96 - 16h

23

step-by-step explanation: