First slide

Instantaneous velocity

Question

The coordinates of a moving particle at time t are given by x = c t² and y = b t². The speed of the particle is given by

Easy

A

2t(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

$\begin{array}{l} \frac{dx}{dt} = 2 ct and \frac{dy}{dt} = 2 bt \\ \begin{aligned} ∴ V & = \sqrt{\{{(\frac{dx}{dt})}^{2} + {(\frac{dy}{dt})}^{2}} \end{aligned} \\ = \sqrt{\{(2 ct)^{2} + (2 bt)^{2}\}} = 2 t \sqrt{(c^{2} + b^{2})} \end{array}$

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