The velocity function is v(t)=t^2−4t+3 for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval [−1,5].

Answer 1

displacement = integral from t = -1 to 5 of vdt

Take the integral from -1 to 5 of (t² - 4t + 3) dt

I'll let you do that. I wish calculus books asked reasonable questions in this regard. 1st, we have negative time and 2nd, the term "net distance" is weird. Displacement is the change in position during the time interval and can have a negative sign. Distance is generally positive definite. They may be looking for a phrase like "a net positive movement" in the + or - direction.

Please consider a tutor. Take care.