Question

Motion of a particle subjected to resistive force solve f=-mkv find velocity and position
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Answer 1

Answer:

f = mkv

dv/dt = mkv

dv/v = mk dt

integrating both sides

ln v = mkt + C

v = e ^ (mkt+ C)

v = P e ^ mkt where P is constant

s = P (mkt) . e^(mkt) + L where L is another constant

Explanation:

Answer 2

Given: f= mkv

To find: Velocity and Position

Solution: f= mkv

here f that is force is a function of velocity of the motion.

and we also know that f= ma where a is acceleration which is equal to dv/dt

so we can say that f= mdv/dt

putting the value of f

mkv= mdv/dt

dv/dt= kv

∫(dv/v) = ∫ (kdt)

ln|v|+c= kt

ln|v|= kt-c where c is arbitrary constant

v= e^(kt-c)

Therefore, the velocity of the motion will be v= e^(kt-c)

we also known that v= dr/dt

dr/dt= e^(kt-c)

dr/dt= ne^kt (where n= e^(-c))

∫dr = ∫ne^kt dt

r= n/k(e^kt) + p

where p is arbitrary constant

Therefore the position of the motion will be

r= e^(-c) /k(e^kt) +p