Find the displacement and distance traveled

Question

The velocity function is v(t)=t²-3t+2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,6].

Answer 1

v(t) = t^2 -3t +2

d(t) = integral of v(t) = t^3/3 - 3t^2/2 + 2t + C

evaluated between t=-1 and t=6

d(6)-d(-1) = 72 - 54 + 12 -[-1/3 - 3/2 -2]

= 30 + 23/6

30+ 3 5/6

= 33 5/6

= displacement

= distance traveled between t=-1 and t=6