Q: The coordinates of a body moving in a plane at any instant of time t are x = α t^{2} and y = β t^{2} . the speed of the body is.

Sol: x = α t^{2}

$\large v_x = \frac{dx}{dt} = 2 \alpha t $

y = β t^{2}

$\large v_y = \frac{dy}{dt} = 2 \beta t $

Speed $\large v = \sqrt{v_x^2 + v_y^2 } $

$\large v = \sqrt{(2 \alpha t)^2 + (2 \beta t)^2 } $

$\large = 2 t \sqrt{\alpha^2 + \beta^2}$