plz help solve this?

Question

the resistance to the motion of a car of mass m is proportional to the square of its velocity.the power being applied is P.How much distance will the car cover while it accelerates from v0 to v.k is the constant of proportionality and resistance=kv2

dis is an iit sum.

Answer 1

F - kmv^2 = m(dv/dt)
F/v - kmv = (m/v)(dv/dt)
P - kmv = (m/v)(dv/dt)
P - kmv = (m/v)(dv/ds)(ds/dt)
P - kmv = m(dv/ds)
ds = mdv/(P - kmv)
let u = P - kmv, du = -kmdv, dv = -du/km
ds = -(m/km)du/u
-ks = Ln(P - kmv)
-k(s - s0) = Ln(P - kmv) - Ln(P - kmv0)
s = s0 + (1/k)Ln[(P - kmv0)/(P - kmv)]

Answer 2

F=ma
F=force(recictance),m+mass,a=acceleration
now here F is kv2
so P-kv2=ma,
a=(P-kv2)/m.
now b formula,
V2=U2+2as,here V is final velocity
U is initial velocity
s is distance travel
(v)2=(v0)2+2((P-kv2)/m).s

s=((v)2-(v0)2)/2((P-kv2)/m).

s=m.((v)2-(v0)2)/2(P-kv2)

hope u understand
good lk

Answer 3

Distance travelled = (K x M x V x V xV) / (4 x P)

Answer 4

It will not travel at all. The car has no tires and no engine.