Solving Dependence of Velocity on Time

[fer Mnaj]

Homework Statement

Given the acceleration as a function of speed a = −kv (v - v_c) (a) Find an expression for speed as a function of time. (b) How would it look a sketch of velocity as a function of time for initial velocities v_o greater than v_c and less than v_c?

Relevant Equations

a = −kv (v - v_c)

I could use some help with this problem. I am having trouble finding how to change the dependence from velocity to time in a).

 

[Chestermiller]

a = dv/dt

 

[PeterDonis]

Im having trouble finding how to change the dependence from velocity to time in a).

What have you tried?

 

[fer Mnaj]

What have you tried?

Hi, so far
a= dv/dt

so
dv/dt=−kv^ 2+(kv_c)v
dv/dt=−kv^ 2+(kv_c)v

dv/dt−(kvc)v=−kv^ 2

 

[PeterDonis]

so far
a= dv/dt

so
dv/dt=−kv^ 2+(kv_c)v
dv/dt=−kv^ 2+(kv_c)v

dv/dt−(kvc)v=−kv^ 2

So what kind of equations are these? (Try moving all of the terms to the LHS and making the RHS zero. What kind of equation do you have?)

 

[fer Mnaj]

So what kind of equations are these? (Try moving all of the terms to the LHS and making the RHS zero. What kind of equation do you have?)

whats RHS and LHS??, I think its bernoulli, isn't it?

 

[PeterDonis]

whats RHS and LHS?

Right Hand Side and Left Hand Side.

 

[darrell1NZ]

fer Mnaj, thanks.

 

[haruspex]

@fer Mnaj , if the rearrangement @PeterDonis suggests does not help you, try rearranging it so that the dt is on one side and all the references to v are on the other.