Kinematics Question 562

Question: The coordinates of a moving particle at any time t are given by x = at3 and y = bt3.The speed of the particle at time t is given by[AIEEE 2003]

Options:

A) $ \sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $

B)$ 3t\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $

C) $ 3t^{2}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $

D)$ t^{2}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $

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Answer:

Correct Answer: C

Solution:

$ x=\alpha t^{3} $ and $ y=\beta t^{3} $ (given) $ v _{x}=\frac{dx}{dt}=3\alpha t^{2} $

and $ v _{y}=\frac{dy}{dt}=3\beta t^{2} $

Resultant velocity$ =v=\sqrt{v _{x}^{2}+v _{y}^{2}}=3t^{2}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $



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