Question Type 4: Accounting for the difference between distance and displacement Exercises

Given the velocity function $v(t) = 5$ m/s for $0 \\le t \\le 3$ s, find (a) the displacement and (b) the total distance traveled over this interval.

A particle moves with velocity $v(t)=2t$ m/s for $0\le t\le 4$ s. Calculate the displacement and the total distance traveled.

For $0\le t\le 3$, a particle has velocity $v(t)=t^{2}-4$ m/s. Find the displacement and total distance traveled.

A particle has velocity

Find its displacement and total distance traveled for $0\le t\le5$.

A particle has velocity $v(t)=\sin t$ m/s for $0\le t\le \pi$. Determine its displacement and total distance traveled.

Find the displacement and total distance for $v(t)=3t^{2}-12t+9$ m/s on $0\le t\le 3$ s.

A particle moves with velocity $v(t)=4\cos(2t)$ m/s for $0\le t\le \pi$. Compute its displacement and total distance traveled.

Given $v(t)=t^{3}-6t^{2}+9t$ m/s for $0\le t\le 4$, find the displacement and the total distance traveled.

A particle moves with velocity $v(t)=t^{2}-8t+12$ m/s on $0\le t\le5$. Find its displacement and total distance traveled.

For $0\le t\le2$, velocity is $v(t)=10e^{-t}-2$ m/s. Compute the displacement and total distance traveled.

Determine the displacement and total distance traveled for $v(t)=4\cos t -2$ m/s over $0\le t\le\pi$.

A particle travels with velocity $v(t)=(t-3)^{2}-4$ m/s over $0\le t\le6$. Find its displacement and total distance traveled.