A particle is moving with a velocity of v0 when s = 0 and t = 0. If it is subjected to a deceleration of a = -kv3, where k is a constant, determine its velocity and position as functions of time. *

Explanation:

Relation between acceleration a , position s and velocity v.

a = dv/dt

dv/dt= -kv3

. dv/v3 = -kdt

By integration above equation -

∫dv/v³ = ∫ -kdt

-1/2v²= -kt + C

C = integration constant

When t = 0 , v = v₀

C = -1/2v²0

So -

1/v² = kt + 1/v²0  

v = v₀/(ksv₀ + 1)