JEE Main Motion in Plane PYQ

Home Courses Contact About

16. (AIEEE 2003 )

The co-ordinates of a moving particle at any time 't' are given by x = $α$ t³ and y = βt³. The speed to the particle at time 't' is given by

A. $3 t \sqrt{α^{2} + β^{2}}$

B. $3 t^{2} \sqrt{α^{2} + β^{2}}$

C. $t^{2} \sqrt{α^{2} + β^{2}}$

D. $\sqrt{α^{2} + β^{2}}$

rrect Option is (B)

Given that $x = α t^{3}$ and $y = β t^{3}$

$∴$ $v_{x} = \frac{d x}{d t} = 3 α t^{2}$

and $v_{y} = \frac{d y}{d t} = 3 β t^{2}$

$∴$ $v = \sqrt{v_{x}^{2} + v_{y}^{2}}$

$= \sqrt{9 α^{2} t^{4} + 9 β^{2} t^{4}}$

$= 3 t^{2} \sqrt{α^{2} + β^{2}}$