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Instantaneous Velocity

A particle mo...

Question

A particle moves on the curve $y = \frac{x^{4}}{4}$ where $x = t / 2$ , x and y are measured in metre and t in second. At $t = 4 s$ , find the velocity of particle.

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Solution

$V_{y} = \frac{d y}{d t} = \frac{d y}{d x} \times \frac{d x}{d t} = x^{3} \times \frac{1}{2} = \frac{t^{3}}{16}$

at $t = 4^{3} V_{y} = \frac{4 \times 4 \times 4}{16} = 4 m / s V_{x} = \frac{1}{2} m / s$

Velocity of particle is $V = V_{x}^i + V_{y}^j = \frac{1}{2}^i + 4^j$

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