First slide

Motion in a plane

Question

The co-ordinates of a moving particle at any time f are given by
$x = {ct}^{2} and y = {bt}^{2}$
The speed of the particle is given by

Easy

A

$2 t (c + b)$
B

$2 t \sqrt{(c^{2} - b^{2})}$
C

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

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

Solution

$\begin{array}{l} v_{x} = \frac{dx}{dt} = 2 ct and v_{y} = \frac{dy}{dt} = 2 bt \\ ∴ v = \sqrt{(v_{x}^{2} + v_{y}^{2})} = 2 t \sqrt{(c^{2} + b^{2})} \end{array}$

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