Solving a Frictionless Cart Problem with Rain

[Gregie666]

hi.
can anyone push me in the right direction with the followin problem, please?

Homework Statement

a cart is moving on a frictionless surface at a speed of $$V_0$$
the mass of the cart is M.
it suddenly starts to rain at time t=0. the rain is dropping vertically at a rate of q gk per second.
the cart collects all the rain drops that hit it.
express the speed of the cart as a function of time passed since it started raining.

Homework Equations

$$F = {{dp} \over {dt}}$$

The Attempt at a Solution

$$<br /> <br /> & F = {{dp} \over {dt}} \Rightarrow \cr <br /> & 0 = {{dm} \over {dt}}v(t) + {{dv} \over {dt}}m(t) \Rightarrow \cr <br /> & 0 = qv(t) + {{dv} \over {dt}}(M + qt) \Rightarrow \cr <br /> & qv = - {{dv} \over {dt}}(M + qt) \Rightarrow \cr <br /> & qvdt = (M + qt)dv <br /> <br />$$

so i get this equation and i don't know how to solve it for v...


**how do i add line breaks to the latex??**

 

[weatherhead]

just like any differential equation, split the variables, put in the initial conditions, and rearrange for the variable you want.

$$\int { \frac {q}{M+qt}} dt = \int {\frac {1}{v}}dv$$

Try it that way