The relation between time t and distance x is t = αx2 + 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
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
