Question

A particle moves along the x-axis with velocity v(t) = t2 − 4, with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 3 seconds.
3
−3
15.333
7.667

Answer 1

The total distance traveled by the particle from t = 0 to t = 3 seconds is given by

$\int\limits^3_0 {(t^2-4)} \, dt =\left[ \frac{t^3}{3} -4t\right]_0^3 \\ \\ = \frac{3^3}{3} -4(3)=9-12=\bold{-3}$