The position of a particle is given by where is in seconds and the coefficients have the proper units for to be in metres. The direction of velocity of the particle at t = 1 s is

Question

The position of a particle is given by $\vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k},$ where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres. The direction of velocity of the particle at t = 1 s is

Smart Achievers · Accepted Answer

(1)

$Given : \vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k}$

$\vec{r}$

$Let θ be the angle which the direction of \vec{v} makes with the x -axis. Then$

$\tan θ = \frac{v_{y}}{v_{x}} = \frac{4 t}{3} = \frac{4}{3}$ $or$ $θ = \tan^{- 1} (\frac{4}{3}) = 53 °$

Solution

Q.
The position of a particle is given by $\vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k},$ where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres. The direction of velocity of the particle at t = 1 s is

1 53° with $x$ -axis

2 37° with $x$ -axis

3 30° with $y$ -axis

4 60° with $y$ -axis

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Solution

Q. The position of a particle is given by r→=3ti^+2t2j^+5k^, where t is in seconds and the coefficients have the proper units for r→ to be in metres. The direction of velocity of the particle at t = 1 s is

1 53° with x-axis

2 37° with x-axis

3 30° with y-axis

4 60° with y-axis