10. Physics Applications of Integrals

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 $0\le t\le 4$.

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\(\le\)4$ 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\(\le\)4$ 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 $[0,\frac{5\pi }{4}]$