- #1

Like Tony Stark

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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.