Question

The velocity function is v(t) = - t^2 + 4 t - 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].

Answer 1

displacement = integral v dt
= -t^3/3 + 2 t^2 - 3 t
from -2 to +6
do the arithmetic

distance traveled
that means always use absolute value of any part of the integral
when is velocity negative and when is it positive?
0 = t^2 - 4 t + 3
0 = (t-3)(t-1)
velocity 0 at t = 1 and t = 3
so:
take absolute value of integral from
-2 to + 1
add to absolute value of integral from +1 to +3
add to absolute value of integral from +3 to + 6

Answer 2

thank you