IB Mathematics Applications & Interpretation Question Type 3: Integrating Kinematic Variables Exercises

A particle moves with velocity $v(t)=t^3-3t^2+t+2{\text{ m s}}^{-1}$. Find the total distance traveled between $t=0$ and $t=4\text{ s}$.

A particle has acceleration $a(t)=6t-2{\text{ m/s}}^2$, with $v(1)=3\text{ m/s}$ and $s(1)=5\text{ m}$. Find the displacement function $s(t)$ and compute $s(4)$.

A cyclist rides so that $v(t)=5\sin t{\text{ m s}}^{-1}$, with $s(0)=0$. Find the net displacement from $t=0$ to $t=\pi$ s.

Given velocity $v(t)=2t^2-t+1\text{ m/s}$, find the acceleration $a(t)$ and the displacement between $t=1\text{ s}$ and $t=3\text{ s}$.

A ball is thrown vertically upward with initial velocity $v_0=20{\text{ m s}}^{-1}$ from ground level. Take $a(t)=-9.8{\text{ m s}}^{-2}$.

Find (a) the time to reach maximum height; (b) the maximum height reached.

A particle has acceleration $a(t)=3t{\text{ ms}}^{-2}$ and initial velocity $v(0)=4{\text{ ms}}^{-1}$.

Find $v(t)$ and the distance traveled from $t=0$ to $t=4$ seconds.

Given velocity $v(t)=t^2-4t+3\text{ m/s}$, find the total distance traveled from $t=0$ to $t=5\text{ s}$.

The displacement of a particle is given by $s(t)=t^4-4t^3+6t^2\text{ m}$ for $t\ge 0$, where $t$ is measured in seconds.

Find its velocity $v(t)$, acceleration $a(t)$, and the times when the particle changes direction for $t\ge 0$.

A particle moves with constant acceleration $a=5{\text{ m s}}^{-2}$, initial velocity $v(0)=2{\text{ m s}}^{-1}$, and initial displacement $s(0)=0\text{ m}$.

Find expressions for $v(t)$ and $s(t)$.

A particle moves with velocity $v(t)=t^3-6t^2+9t{\text{ m s}}^{-1}$. Determine the total distance traveled between $t=0$ and $t=3\text{ s}$.