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} $
