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Instantaneous Velocity

A particle mo...

Question

A particle moves in such a manner that $x = A t, y = B t^{3} - 2 t, z = c t^{2} - 4 t$ , where $x, y$ and $z$ are measured in metres and $t$ is measured in seconds, and $A, B$ and $C$ are unknown constants. Given that the velocity of the particle at $t = 2 s$ is $\to v = (\begin{matrix} \frac{d \to r}{d t} \end{matrix}) = 3^i + 22^j m / s$ , determine the velocity of the particle at $t = 4 s$ .

8^i + 94^j + 4^k m / s

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6^i + 94^j + 6^k m / s

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3^i + 94^j + 4^k m / s

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3^i + 92^j + 4^k m / s

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Solution

The correct option is A $3^i + 94^j + 4^k m / s$
$\to v = A^i + (3 B t^{2} - 2)^j + (2 c t - 4)^k$
At $t = 2, A^i + (12 B - 2)^j + (4 c - 4)^k = 3^i + 22^j$
Thus, $A = 3, B = 2, C = 1$
$∴ \to v = 3^i + (6 t^{2} - 2)^j + (2 t - 4)^k$
At $t = 4, \to v = 3^i + (96 - 2)^j + (8 - 4)^k = 3^i + 94^j + 4^k$

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