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A 5kg mass freely falling and experiencing a retarding force of 5v where v is the speed in m/sec has
Asked by sreekarreddypindi | 30 May, 2022, 12:15: PM
Force acting on a freely falling body is written as

where m is mass of body , v is velocity at timt t , dv/dt is acceleration i.e., rate of change of velocity,
g is acceleration due to gravity and b is velocity coefficient of resistive force acting on the body.

( units of b is kg/s )

Above equation is written as

Let b/m = k . ( Units of k is s-1 )

By integrating above expression on both sides with initial condition v = 0 at t = 0, we get

ln( g - k v ) - ln(g) = - k t

In above expression , k = b/m = 5 kg s-1/ 5 kg  = 1 s-1

Hence we get velocity v as a function of time as

v = g ( 1 - e-t )

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