Question

The coordinates of a moving particle at any time are given by $x = at^{2}$ and $y = bt^{2}$. The speed of the particle at any moment is

• A. $2t(a + b)$
• B. $2t\sqrt{(a^{2} - b^{2})}$
• C. $t\sqrt{a^{2} + b^{2}}$
• D. $2t\sqrt{(a^{2} + b^{2})}$

Answer 1

Answer: (D)

$2t\sqrt{(a^{2} + b^{2})}$

Answer 2

Velocity along X-axis $v_{x} = \frac{dx}{dt} = 2at$

Velocity along Y-axis $v_{y} = \frac{dy}{dt} = 2bt$

Magnitude of velocity of the particle,

$v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 2t\sqrt{a^{2} + b^{2}}$