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Motion in one dimension Problem

The relation between time t and distance x is t = αx+ βx, where α & β are constants, then the retardation is

Sriyathmika asked

Asnwer

Given  t = αx2 + βx

Differentiate both sides with respect to time (t)
dt/dt = 2αx.dx/dt + β.dx/dt
1 = 2αxv + βv
v.(2αx + β) = 1
(2αx + β) = 1/v
Again differentiate both side with respect to time (t)
2α.dx/dt = -v -2 . dv/dt
2αv = v -2 . acceleration
acceleration = -2αv 3
Hence, retardation= 2αv 3

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