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Homework Statement:

A block of mass ##100 kg## is moving with velocity ##27,7 \frac{m}{s}##, which reduces to ##15 \frac{m}{s}## after a distance of ##200 m##. This change in velocity is caused by a force ##Fr=cv^2## where ##c## is a constant and ##v## the velocity.
Find the value of the constant, the time that it takes to move the distance given and an expression for velocity in function of position.
Relevant Equations:
 ##Fr=m.a##
##Fr=m.a##
##cv^2=m.a##
##cv^2=m.\frac{dv}{dt}##
##dt=\frac{m}{cv^2} dv##
After integrating, I get
##t=\frac{m}{c.v}\frac{m}{c.v_0}##
Then, solving for ##v## we get
##v=\frac{m.v_0}{v_0.t.c+m}##
##\frac{dx}{dt} = \frac{m.v_0}{v_0.t.c+m}##
After integrating that, I get an expression for ##x(t)##.
But how can I get the constant and the time? Because they are unknowns and if I try to use ##t(v)## and ##x(t)## I get an equation which I can't solve.
##cv^2=m.a##
##cv^2=m.\frac{dv}{dt}##
##dt=\frac{m}{cv^2} dv##
After integrating, I get
##t=\frac{m}{c.v}\frac{m}{c.v_0}##
Then, solving for ##v## we get
##v=\frac{m.v_0}{v_0.t.c+m}##
##\frac{dx}{dt} = \frac{m.v_0}{v_0.t.c+m}##
After integrating that, I get an expression for ##x(t)##.
But how can I get the constant and the time? Because they are unknowns and if I try to use ##t(v)## and ##x(t)## I get an equation which I can't solve.