IB Mathematics Applications & Interpretation Question Type 4: Accounting for the Difference Between Distance and Displacement Exercises

Determine the displacement and total distance traveled by a particle moving with velocity $v(t)=4\cos t-2{\text{ m s}}^{-1}$ over the interval $0\le t\le \pi$.

A particle travels with velocity $v(t)=(t-3{)}^2-4{\text{ m s}}^{-1}$ over the interval $0\le t\le 6$.

Find its displacement and total distance traveled.

A particle moves in a straight line with a velocity given by $v(t)=t^2-8t+12$ m s${}^{-1}$ for $0\le t\le 5$.

Find the displacement of the particle and the total distance it travels in the first 5 seconds.

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

A particle's velocity $v$ in ${\text{m s}}^{-1}$ at time $t$ seconds is given by $$v(t)=\{\begin{array}{ll}4,& 0\le t\le 2\\ -2,& 2<t\le 5\end{array}$$ Find the particle's displacement and total distance traveled in the interval $0\le t\le 5$.

Given $v(t)=t^3-6t^2+9t{\text{ m s}}^{-1}$ for $0\le t\le 4$, find the displacement and the total distance traveled.

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

A particle moves with velocity $v(t)=4\cos (2t){\text{ m s}}^{-1}$ for $0\le t\le \pi$. Find its displacement and the total distance traveled.

A particle moves along a straight line such that its velocity $v$ at time $t$ seconds is given by $v(t)=3t^2-12t+9$, for $0\le t\le 3$.

Find the displacement and the total distance travelled by the particle.

Compute the displacement and total distance traveled by the particle in this time interval.

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