The velocity ($\mathrm{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le 4$ hours. Let $s\left(0\right)=0$.
Determine $s\left(t\right)$ for $0\le t\le 4$.

A particle moves along the $x$-axis and its acceleration is given by $a\left(t\right)=\cos \pi t$.

Find $v\left(t\right)$ if $v\left(0\right)=0$

A particle moves along the $x$-axis and its acceleration is given by $a\left(t\right)=\cos\pi t$.

Find $s\left(t\right)$ if $s\left(0\right)=1$

A rock is thrown from a height of $2\mathrm{ft}$ with an initial speed of $25\mathrm{ft}$/$s$. Acceleration resulting from gravity is $-32\mathrm{ft}$/$s^2$.

Find $v\left(t\right)$

A rock is thrown from a height of $2\operatorname{ft}$ with an initial speed of $25\operatorname{ft}$/$s$. Acceleration resulting from gravity is $-32\operatorname{ft}$/$s^2$.

Find $s\left(t\right)$

The velocity ($\operatorname{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le4$ hours. Let $s\left(0\right)=0$.

How far does the drone travel during the first hour?

The velocity ($\operatorname{mi}$/$hr$) of a drone flying in the air is given by $v\left(t\right)=12+4t^2$ for $0\le t\le4$ hours. Let $s\left(0\right)=0$.

How far has the drone traveled by the time it has reached $48\mathrm{mi}$/$hr$?

Suppose that a particle travels along the $x$-axis and its velocity is given by $v\left(t\right)=2\cos t$ for $0\le t\le 2\pi$.

Find the particle's displacement on $[0,\frac{5\pi }{4}]$

Suppose that a particle travels along the $x$-axis and its velocity is given by $v\left(t\right)=2\cos t$ for $0\le t\le2\pi$.

Find total distance traveled by the particle on $\left\lbrack0,\frac{5\pi}{4}\right\rbrack$.