Question

A particle moves along a line so that its posistion at any t is greater than or equal to 0 is given by the function s(t)= t^3-8t+1, where s is measured in feet and t is measured in seconds.

a) find the displacement during the first three seconds

b) Find the average velocity during the first three seconds

c) Find the instantaneous velocity when t=3 seconds

d) find the accelteration of the object when t=3 seconds

e) At what value or values of t does the particle change direction?

Answer 1

a) find s(3) - s(0)

b) avg vel in first 3 sec = (s(3) - s(0))/3

c) find derivative of s(t), then sub in t = 3

d) find derivative of c) result, sub in t=3

e) mmmh, one of those derivatives (velocity or acceleration ) must be zero when I change direction ...