Question

A 1500 kg car located at $<300,0,0>\mathbf{m}$ has a momentum of $<45000,0,0>\mathbf{kg}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$ . What is its location 10 s later?

Short answer

The location of the car 10 slater is .

Step-by-step solution

Given data

Mass of the car is, $m=1500\mathrm{kg}$.

The initial location of the car was .

The momentum of the car is .

Time after which location is to be the measure is, $t=10\mathrm{s}$.

Momentum and uniform motion

$$\begin{gathered} \mathbf{The}\mathbf{}\mathbf{displacement}\mathbf{}\mathbf{in}\mathbf{}\mathbf{time}\mathbf{}\mathit{t}\mathbf{}\mathbf{of}\mathbf{}\mathbf{a}\mathbf{}\mathbf{body}\mathbf{}\mathbf{of}\mathbf{}\mathbf{mass}\mathbf{}\mathit{m}\mathbf{}\mathbf{}\mathbf{and}\mathbf{}\mathbf{having}\mathbf{}\mathbf{uniform}\mathbf{}\mathbf{momentum}\mathbf{} \\ \mathit{p}\mathbf{}\mathbf{can}\mathbf{}\mathbf{be}\mathbf{}\mathbf{written}\mathbf{}\mathbf{as}\mathbf{,} \end{gathered}$$

role="math" localid="1668493070077" ${\overrightarrow{\mathbf{r}}}_{\mathbf{f}}\mathbf{-}{\overrightarrow{\mathbf{r}}}_{\mathbf{i}}\mathbf{=}\frac{\overrightarrow{\mathbf{p}}}{\mathbf{m}}\mathit{t}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\left(1\right)$

Here ${\overrightarrow{\mathbf{r}}}_{\mathbf{f}}$is the final location of the car.

Determining the final location of the body

The momentum vector of the car is, $\overrightarrow{p}=45000\hat{i}\mathrm{kg}·\mathrm{m}/\mathrm{s}$.

From equation (1), the final location can be calculated as,

Thus, the required location is .