Question

a body moves in a plane so that the displacement along x and y axis is X is equal to 3t^2 and Y is equal to 4t^2 then velocity is

Answer 1

as we know that velocity is the first derivative of displacement 
so for the total velocity 
dx|dt=6t
dy|dt=8t

Answer 2

The answer to the question is 10t.

CALCULATION:

As per the question, the displacement along X axis x = $3t^2$.

Hence, the velocity of the body along X -axis $V_{x} =\frac{dx}{dt}$

                                                                                  $=\frac{d}{dt}(3t^2)$

                                                                                  $=6t$

The displacement along Y- axis is given as   $V_{y} =\frac{dy}{dt}$

                                                                           = $\frac{d}{dt}(4t^2)$

                                                                           = 8t.

We are asked to calculate the velocity.

The velocity of the body is calculated as -

                           velocity V = $\sqrt{(V_{x})^2+(V_{y})^2$

                                             = $\sqrt{(6t)^2+(8t)^2}$

                                             = $\sqrt{36t^2+64t^2}$

                                             = $\sqrt{100t^2}$

                                             = $10t$             [ans]