Question

The coordinates of a moving particle at time t are given by x= ct^2 and y=bt^2. The speed of the particle is given by

Answer 1

Given :

The coordinates of a moving particle at time t are given by x = ct² and y = bt².

To Find :

Speed of the moving particle.

Solution :

■ In order to find speed of the particle, we have to differentiate the given position equations.

As we know that, v = dx/dt or dy/dt

❇ x coordinate of the speed :

➙ v(x) = dx/dt

➙ v(x) = d(ct²)/dt

➙ v(x) = 2ct

❇ y coordinate of the speed :

➙ v(y) = dy/dt

➙ v(y) = d(bt²)/dt

➙ v(y) = 2bt

Resultant speed of the particle :

$:\implies\tt\:v=\sqrt{(v_x)^2+(v_y)^2}$

$:\implies\tt\:v=\sqrt{(2ct)^2+(2bt)^2}$

$:\implies\tt\:v=\sqrt{4c^2t^2+4b^2t^2}$

$:\implies\tt\:v=\sqrt{4t^2(b^2+c^2)}$

$:\implies\:\underline{\boxed{\bf{\purple{v=2t\sqrt{b^2+c^2}}}}}$