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The coordinates of a particle moving in x - y plane at any instant of time t are $x = 4t^{2}$; $y = 3t^{2}$. The speed of the particle at that instant is
Explanation
According to the question, at any instant t, $x = 4t^{2}$, $y = 3t^{2}$ $\therefore v_{x} = dx/dt = d/dt(4t^{2}) = 8t$ and $v_{y} = dy/dt = d/dt(3t^{2}) = 6t$ The speed of the particle at instant t. $v = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{{(8t)}^{2} + {(6t)}^{2}} = 10t$