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Power, Force and Velocity

The position ...

Question

The position vector of a particle is given by $\to r = 1.2 t^i + 0.9 t^{2}^j - 0.6 (t^{3} - 1)^k$ where $t$ is the time in seconds from the start of motion and where $\to r$ is expressed in metres.
Determine the power $(\begin{matrix} P = \to F . \to v \end{matrix})$ in watts produced by the force $\to F = (\begin{matrix} 60^i - 25^j - 40^k \end{matrix}) N$ which is acting on the particle at time $t = 4$ seconds.

A

1044 W

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B

10.44 W

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C

2088 W

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D

20.88 W

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Solution

The correct option is A $1044 W$
$\to v = \frac{d \to r}{d t} = 1.2^i + 1.8 t^j - 1.8 t^{2}^k$
At $t = 4 s, \to v = 1.2^i + 7.2^j - 28.8^k$
$P = \to F . \to v = (\begin{matrix} 60^i - 25^j - 40^k \end{matrix}) \cdot (\begin{matrix} 1.2^i + 7.2^j - 28.8^k \end{matrix})$
$= 1044 W$

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