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a point 'p' moves in countrclock wise direction on a circular path .the movement of 'p' such that it sweeps a length of ''s=t(cube)+5 where 's'in mtrs and 't' in secnds .the radius of path is 20 m . the acceleration of 'p' when t=2 sec is nearly
a)14 b)13 c)12 d)7.2 ans:
s = t3 + 5
velocity =dr/dt & tengential accletarion (aT) = dv/dt
so
v = 3t2
aT= 6t
when a particle is in circular motion then , centripital accleration(ac) acts along center & tangential accleration acts along tangent perpendicular to ac...
net accleration = (aT2 + ac2)1/2 ...........1
ac = v2/r
at t=2 sec , v=12m/s
so ac = (12)2/r =144/20 = 7.2m/s
now at t=2sec
aT = 12m/s2
putting aT & ac in eq 1
we get total acc = (122 + 7.22)1/2 = 13.99 =14m/s2
14.differentiate s to get v.v square/r is radial acceleration and dv/dt is tangential one.root over the square of both the accelerations give you the answer
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