Question

The position of an object moving vertically along a line is given by the function s(t)=−16t2

+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.

Answer 1

`\\$Velocity = $(Displacement)/(total time)$;`

`s(t) = -16t^2+128t\\\\$a) \\$Vel_1 = (s(4) - s(1))/(4 - 1) = (144)/(3) = 48\\$b)\\$Vel_2 = (s(3) - s(1))/(3-1) = (128)/(2) = 64\\$c)\\$Vel_3 = (s(2) - s(1))/(2-1) = (80)/(1) = 80\\$d)\\$Vel_4 = (s(1+h) - s(1))/(1+h-1) = (-4h(h+6))/(h) = -4h - 24`