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Question

The co-ordinates of a particle restricted to move in a plane is given by
X=6 cosπt
y=14cos2 πt
The magnitude of acceleration of particle at t=1.5 s is (where x and y are in meter and t is in seconds)

A
Zero
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B
6π2 m/s2
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C
16π2 m/s2
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D
8π2 m/s2
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Solution

The correct option is C 16π2 m/s2
Given,
x=6cosπt
y=14cos2πt
Velocity along x-axis,
vx=dxdt=6πsinπt

Acceleration along x-axis,
ax=dvxdt
ax=6π2cosπt
ax|t=1.5sec=6π2cos(1.5π)
ax|t=1.5sec=6π2×0=0m/s2
Velocity along y-axis,
vy=dydt=+8π2sin2πt

Acceleration along y-axis,
ay=dvydt
ay=16π2sin2πt
ay|t=1.5sec=16π2sin(3π)=16π2×(1)
ay|t=1.5sec=16π2

Acceleration, a=a2x+a2y
a=(0)2+(16π2)2
a=16π2m/s2
The correct option is C.

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