wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
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

Open in App
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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon