Displacement Calculus

Question

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2 − 2t − 8, 2 ≤ t ≤ 8 (a) Find the displacement (in meters). (b) Find the distance traveled (in meters) by the particle during the given time interval.

Answer 1

v(t) = t^2 -2t -8 = (t-4)(t+2)

s(t) = integral of v(t) = t^3-t^2 -8t +C

s(8) = 8^3 -64 -64 + C = C+512-128= C+384

s(2) = 2^3 -2^2 -8(2) + C = C+8-4-16 = C +-12

displacement = s(8)-s(2) = 42 2/3 meters

s(4) = 4^3-4^2-8(4) +C = C-26 2/3

distance traveled = 22 2/3 +73 1/3= 96 meters