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Vector Component

The coordinat...

Question

The coordinates of a particle moving in x-y plane at any time t are $(2 t, t^{2})$ . Find (a) the trajectory of the particle, (b) velocity of particle t and (c) acceleration of particle at any time t.

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Solution

$x = 2 t, y = t^{2} x^{2} = 4 t^{2} = 4 y \Rightarrow x^{2} = 4 y i s t h e t r a j e c t o r y v_{x} = \frac{d x}{d t} = 2 v_{y} = \frac{d y}{d t} = 2 t v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 2 \sqrt{1 + t^{2}} a_{x} = \frac{d^{2} x}{d t^{2}} = 0 a_{y} = \frac{d^{2} y}{d t^{2}} = 2 \Rightarrow a = \sqrt{a_{x}^{2} + a_{y}^{2}} = 2$

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