Kinematics Question 594

Question: The coordinates of a particle moving in x-y plane at any instant of time t are $ {x = 4}{{{t}}^{{2}}}{; y = 3}{{{t}}^{{2}}} $ . The speed of the particle at that instant is

Options:

A) 10 t

B)5 t

C) 3 t

D)2 t

Show Answer

Answer:

Correct Answer: A

Solution:

[a] According to the question, at any instant t,

$ x=4t^{2},y=3t^{2} $

$ \therefore {v _{x}}=\frac{dx}{dt}=\frac{d}{dt}( 4t^{2} )=8t $

and ${v _{y}}=\frac{dy}{dt}=\frac{d}{dt}( 3t^{2} )=6t $

and ${{v _{y}}}=\frac{dy}{dt}=\frac{d}{dt}( 3t^{2} )=6t $

The speed of the particle at instant t..

$ {v}{=}\sqrt{v _{x}^2 +v _{y^2}}{=}\sqrt{{{( {8t} )}^{{2}}}{+}{{( {6t} )}^{{2}}}}{=10}{t} $



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