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Question

For a particle moving along a circle of radius 8 m, the time dependent tangential acceleration is given by at=kt2 m/s2 . Initially, if the particle is at rest and the total acceleration of the particle makes 45 with the tangential acceleration after 2 sec, the value of k (in m/s4 is

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Solution


Given that angle between total acceleration and tangential acceleration is 45 and tangental acceleration varies with time as at=kt2
tanθ=arat
at=ar
[since θ=45 and tan45=1]
Taking at=kt2=dvdt
dv=kt2dt
Integrating on both sides, v0dv=20kt2dt
v=kt33|20=8k3
ar=v2r=(8k3)28=64k29×8=8k29
at=kt2 (at t=2 s) =4k

Since at=ar(at t=2 sec),
4k=8k29
k=4×98=4.5 m/s4

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