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Question

The x and y coordinates of a particle moving in a plane are given by x(t)=acos(pt) and y(t)=bsin(pt) where a, b(<a) and p are positive constants of appropriate dimensions and t is time. Then, which of the following is not true?

A
The path of the particle is an ellipse
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B
Velocity and acceleration of the particle are perpendicular to each other at t=π2ρ
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C
Acceleration of the particle is always directed towards a fixed point
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D
Distance travelled by the particle in time interval between t=0 and t=π2P is a
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Solution

The correct option is D Distance travelled by the particle in time interval between t=0 and t=π2P is a
x=acos(pt),y=bsin(pt)
x2a2+y2b2=1, i.e., equation of ellipse
Now, r=x^i+y^j=acos(pt)^i+bsin(pt)^j
v=drdt=pasin(pt)^i+pbcos(pt)^j
a=dvdt =p2acos(pt)^i=p2bsin(pt)^j
at t=π2p
v=pa^i and a=p2b^j
v perpendicular to a
Also, a=p2r, i.e., directed towards a fixed point.

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