The position of a particle is given by r(t) = 4ti + 2t²j + 5k where t… | NEET 2023

Q17NEET 2023Easy

Velocity, Acceleration & Variable Motion

The position of a particle is given by

$\vec{r}(t) = 4t\hat{i} + 2t^2\hat{j} + 5\hat{k}$

where $t$ is in seconds and $r$ in metre. Find the magnitude and direction of velocity $v(t)$ , at $t = 1\text{ s}$ , with respect to $x$ -axis

Show answer and solution

Answer: (a)

$\vec{v} = \frac{d\vec{r}}{dt} = 4\hat{i} + 4t\hat{j}$ ; at $t = 1$ s, $\vec{v} = 4\hat{i} + 4\hat{j}$ .
$|\vec{v}| = \sqrt{16 + 16} = 4\sqrt{2}$ m/s
$\tan\theta = \frac{4}{4} = 1 \Rightarrow \theta = 45^\circ$ with the $x$ -axis
So the answer is (a).

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