A particle moves in a straight line with velocity 8 − 4 t ft/s. Find the total displacement and total distance traveled over the time interval [0,7]

Question

A particle moves in a straight line with velocity 8−4t ft/s. Find the total displacement and total distance traveled over the time interval [0,7]

I already got the displacement = -42, but what is the distance?

Distance=???

Answer 1

v = 8 -4t

d(t) = the integral of v(t) = 8t - 2t^2 + c where c is an unknown constant which cancels out so it's irrelevant

evaluate the integral from 0 to 7

8(7) -2(7)^2 + c - 8(0) +2(0)^2 - c = 56 -98 = - 42

displacement is - 42

"distance" usually means the absolute value or positive number, |-42| = +42