IB Mathematics Applications & Interpretation Question Type 2: Finding Specific Conditions on the Rate of Change of a Kinematic Variable Exercises

For $s(t)=5t-\frac{1}{t},t>0$, find the intervals on which the acceleration is positive.

Given $s(t)=e^{2t}-4t$, find all times $t$ such that the object is instantaneously at rest.

Let $s(t)=\ln t+t^{-1},t>0$. Find the inflection points of the motion (i.e. where $a^{\prime }(t)=0$).

Given $s(t)=t^3-6t^2+9t$, determine the intervals on which the object is moving to the right (i.e., $v(t)>0$).

For the position function $s(t)=e^{-t}+\frac{\sin (-t)}{t}$, $t>0$, find the first positive time $t$ at which the object is at rest.

Consider $s(t)=t\ln t-t$, for $t>0$, where $s$ is the displacement of a particle at time $t$.

Find the values of $t$ at which the speed of the particle is equal to $1$.

For $s(t)=\frac{t^2}{2}+3\ln t,t>0,$ find the time at which the speed is minimized.

An object moves along a straight line such that its displacement, $s$ metres, from a fixed point $O$ at time $t$ seconds, $t\ge 0$, is given by $s(t)=t^4-4t^3+6t^2$.

Determine the times, if any, when the object changes direction.

Let $s(t)=\frac{1}{3}{t}^3-t$ be the displacement of a particle at time $t$. Find the time at which the velocity attains its minimum value.

For the motion $s(t)=2\sin t-t$, find the times when the acceleration is zero.

An object moves with displacement $s(t)=e^{-t}\cos t$. Find the first positive value of $t$ for which the acceleration is zero.

Let $s(t)=\sqrt{t},t\ge 0$. Determine for which $t$ the acceleration is decreasing.