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}}} $
Show Answer
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}}} $
