Question

a particle was moving in the positive x directions has a velocity v. the particle undergoes retardation kv2.where​

Answer 1

The velocity of the particle as function of time is given as v = v₀/(1 + kv₀t)

Explanation :

Given the retardation of the particle ,

a = -kv²

=> dv/dt = -kv²

=> dv/v² = -kdt

integrating both the sides we get,

-1/v = -kt + C

or

1/v = kt + C

Given at initial condition, t = 0 and v = v₀

putting these values in the above equation,

1/v₀ = 0 + C

=> C = 1/v₀

putting the value of C in the above equation,

1/v = kt + 1/v₀

=> 1/v = (1 + kv₀t)/v₀

=> v = v₀/(1 + kv₀t)

Hence the velocity of the particle as function of time is given as v = v₀/(1 + kv₀t)

Answer 2

Answer:

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