Question

he velocity function is v(t)=−t2+6t−8 for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval [-1,5].

displacement=?

Answer 1

-18?

Answer 2

displacement can be found by integrating velocity. v(t) = dx(t)/dt. So, the integral of v(t) is x(t)=-(1/3)t^3+3t^2-8t+C. Since it's between -1 and 5, it is a definite integral so \[\int\limits_{-1}^{5}v(t)=x(t)=-18\]