Equation of Motion for a Particle: Finding Acceleration in Terms of Velocity

[Warr]

Here's the question

The equation of motion of a particle moving in a straight line is:

$$s = kv^2ln v$$

where k is a constant and v is the velocity. Find an equation that expresses the acceleration in terms of velocity.

I need some help on this problem. I'd post my work but I don't exactly have time, and I need to know how to do this by tomorrow morning.

The answer is $$a = \frac {1}{k(1+2ln v)}$$

Thanks in advance, Warr

 

[e(ho0n3]

Apply the Chain Rule

Let $u = v^2\ln{v}$ and then use the chain rule (and remember that $v = ds/dt$ and $a = dv/dt$).

 

[cookiemonster]

Differentiate both sides of the equation with respect to t.

Note that the left hand side will turn into velocity, and the right hand side will turn into some function of v and dv/dt (i.e. acceleration).

Now solve for a.

cookiemonster

 

[Warr]

Thanks guys, I completely forgot that dv/dt was a!

 

[Gokul43201]

There's another neat way to do this.

Notice that a=dv/dt=(dv/dx)(dx/dt)=v(dv/dx)

Since you have x=f(v), find dx/dv and invert it to get dv/dx. Multiply this by v and you have your answer !

 

[JohnDubYa]

So when v = 0...?