Question Type 3: Going from acceleration and velocity, to velocity and displacement Bootcamps

Given the acceleration function $a(t)=4$ m/s², with initial velocity $v(0)=2$ m/s and initial displacement $s(0)=1$ m, find the displacement function $s(t)$.

An object with $v(t)=5t^2$ m/s starts from rest at $s(0)=0$. Find $s(t)$.

An object has acceleration $a(t)=6t-4$ m/s². Given $v(1)=5$ m/s, find the velocity function $v(t)$.

A particle moves with velocity $v(t)=t^3-3t^2+t+4$ m/s. Find its total distance traveled between $t=0$ and $t=2$.

Find the displacement of an object on $[0,3]$ if its velocity is $v(t)=3t^2-2t+1$ m/s.

Given $v(t)=\dfrac{5}{t+1}$ m/s, find the displacement from $t=0$ to $t=4$.

Given $a(t)=6t-4$ m/s², $v(1)=5$ m/s and $s(1)=2$ m, find the displacement function $s(t)$.

If $v(t)=4\cos(2t)$ m/s, find the displacement from $t=0$ to $t=\pi/2$.

A ball is thrown upward so that $a(t)=-9.8$ m/s², $v(0)=20$ m/s and $s(0)=0$. Determine its maximum height.

A particle has acceleration $a(t)=2\sin t$ m/s² and initial conditions $v(0)=0$, $s(0)=0$. Find its displacement on $[0,\pi]$.

An object has acceleration $a(t)=8e^{-2t}$ m/s² and initial velocity $v(0)=3$ m/s. Find (a) $v(t)$, (b) the total displacement as $t\to\infty$.