Question

The position of a particle is given by$\text{r}=3.0t\hat{\text{i}}-2.0t^2\hat{\text{j}}+4.0\hat{\text{k}}m$where t is in seconds and the coefficients have the proper units for $\text{r}$ to be in metres(a) Find the $\text{v}$ and $\text{a}$ of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

Answer 1

(a)

$\overrightarrow{v}\left(t\right)=d\overrightarrow{r}/dt$

$=3.0\hat{i}-4.0t\hat{j}$

$\overrightarrow{a}\left(t\right)=d\overrightarrow{v}\left(t\right)/dt$

$=-4.0\hat{j}$

(b)

$\overrightarrow{v}\left(2\right)=3.0\hat{i}-8.0\hat{j}$

$v\left(2\right)=8.54m/s$

$\angle v\left(2\right)=ta{n}^{-1}(-8/3)=-{69.44}^{\circ }withxaxis$