a car rides in a merry-go-around turning with uniform circular motion. At time t

Question

a car rides in a merry-go-around turning with uniform circular motion. At time t1=2.2 2) A cat rides a merry-go-round turing with uniform circular motion. At time t1-2.2psech cat's velocity (in m/s) is 3.80% 2.60) measured on a horizontal xy coordinate system. At 2-4.40 sec, its velocity is -3.80 i-2.60 j. Assuming that t2-t1 is less than a period of the motion, what is the magnitude of the cat's centripetal acceleration? aConstant C) 2.32 m/s 3.87 +2 A) 6.57 m/s2 B) 9.81 m/s2 D) 11.4 m/s 2 aE) 83.2 m's 2

Explanation / Answer

Here ,

as the velocities are in oposite direction in at the given points

the particle will be at diameterically oposite points

hence , time period , T = 2 * (t2 - t1)

T = 2 * (4.4 - 2.2) = 4.4 s

T = 4.4 s

magnitude of velocity , v = sqrt(3.80^2 + 2.6^2)

v = 4.60 m/s

Now, for the radius

T = 2pi * r/v

4.4 = 2pi * r/4.60

r = 3.22 m

centripetal acceleration = v^2/r

centripetal acceleration = 4.60^2/3.22

centripetal acceleration = 6.57 m/s^2

the centripetal acceleration is (A) 6.57 m/s^2

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