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Question

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 5.00 s, it is at point (5.00 m, 6.00 m) with velocity (3π m/s)^j and acceleration in the positive x direction. At time t2 = 10.0 s, it has velocity (-3π m/s)^i and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path if t2 - t1 is less than one period?


A

(15 m, 6 m)

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B

(-5 m, 6)

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C

(15 m, 0)

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D

(-5 m, 0)

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Solution

The correct option is A

(15 m, 6 m)


We know the body is undergoing uniform circular motion,

only possible path is

As acceleration should always be directed toward the centre

To calculate the position of the centre, we need the radius, to calculate radius,v=ωr we can use the relation,as we can calculate ω
Δθ=3π2,Δt=5s
=3π2×5=3π10S1
using v=ωr
r=vω
|v|=3πm/s given
r=3π3π10=30π3π=10m
if r=10m, coordinates of the centre (15 m,6m)

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