Physics Two Dimensional Motion Question 110
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)$ 3,t\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}} $ C) $ 3,t^{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}}} $
BETA
