Question

A particle moves so that its position (in meters) as a function of time (in seconds) is . Write expressions (in unit vector notation) for (a) its velocity and (b) its acceleration as functions of time.

Answer 1

Answer:

a.Velocity=$\vec{v}=(6t)\hat{j}+8\hat{k}$

b.$\vec{a}=6\hat{j}$

Explanation:

We are given that

A particle moves so that its position (in m) as  function of time is

$\vec{r}=2\hat{i}+(3t^2)\hat{j}+(8t)\hat{k}$

a.We have to find its velocity

We know that

Velocity,$v=\frac{dr}{dt}$

Using the formula

Velocity,v=$\frac{d(2i+3t^2j+8tk)}{dt}$

Velocity=$\vec{v}=(6t)\hat{j}+8\hat{k}$

b.Acceleration$=\vec{a}=\frac{d\vec{v}}{dt}$

$\vec{a}=\frac{d((6t)\hat{j}+8\hat{k})}{dt}$

$\vec{a}=6\hat{j}$