An object of mass m is moving to the right and has a speed of v anda position of

Question

An object of mass m is moving to the right and has a speed of v anda position of x_0 at t=0. A drag force of F_d=cv^2 acts on theobject.

(a) Find the velocity of the particle as a function oftime
(b) Find the position of the particle as a function of time


So I tried this:
F_d= cv^2=ma
so a=cv^2/m
dv/dt=cv^2/m
dv=(cv^2/m)dt
intergrated both sides with respect to time
to get
-1/v(t)=ct/m + C
to get C I get t=0
and got c=1/v_0
Solving for v(t) I got
v(t)=-m/ct +v_0
as my final answer for (a)
What is wrong with this answer?
[It's wrong]

I solved b a similar way and got v(t)=(-m/c)ln(-ct/m + 1/v_0) + x_0+ ln(1/v_0)(m/c)
thats wrong too though

Any help would be greatly appreciated!
Solving for v(t) I got
v(t)=-m/ct +v_0
as my final answer for (a)
What is wrong with this answer?
[It's wrong]

I solved b a similar way and got v(t)=(-m/c)ln(-ct/m + 1/v_0) + x_0+ ln(1/v_0)(m/c)
thats wrong too though

Any help would be greatly appreciated!

Explanation / Answer

Looks OK up to -1/v(t)=ct/m + C
At t = 0      v = v0 v = -1 / (c t / m + K)      using Kas constant of integration K = -1 / v0 v = -1 / (c t / m -1 / v0)  = -mv0 / (c v0 t - m) Then x will be F(ln t) v = -1 / (c t / m -1 / v0)  = -mv0 / (c v0 t - m) Then x will be F(ln t)

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