The position of a particle $x$ (in metre) at a time $t$ second is given by the relation $r = \left( 3t\widehat{\mathbf{i}} - t^{2}\widehat{\mathbf{j}} + 4\widehat{\mathbf{k}} \right).$ Calculate the magnitude of velocity of the particle after 5 s.

Question

Dr. Abubacker · Accepted Answer

(d) Given, $\mathbf{r} = 3t\widehat{\mathbf{i}} - t^{2}\widehat{\mathbf{j}} + 4\widehat{\mathbf{k}}$
$	herefore\ \ \ \ \ \ \frac{d\mathbf{r}}{dt} = \mathbf{v} = 3\widehat{\mathbf{i}} - 10\widehat{\mathbf{j}}$
At $t = 5\ s$
$\mathbf{\ \ \ \ \ \ \ \ \ \ v} = 3\widehat{\mathbf{i}} - 10\widehat{\mathbf{j}}$
$v = \sqrt{(3)^{2} + (10)^{2}} = \sqrt{109} = 10.44\ m/s$

Q. The position of a particle $x$ (in metre) at a time $t$ second is given by the relation $r = \left( 3t\widehat{\mathbf{i}} - t^{2}\widehat{\mathbf{j}} + 4\widehat{\mathbf{k}} \right).$ Calculate the magnitude of velocity of the particle after 5 s.

Explanation

Reviewed by Dr. Abubacker

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