Force given velocity as function of space.

[deblimp]

Homework Statement

The speed of a particle of mass m varies with space as v(x) =ax^-n
v(x=0)=0 at t=0.
Find F(x).

Homework Equations

F=ma=m dv/dt

The Attempt at a Solution

I am not really sure where to start from. Would x(t) or f(t) be relevant?

 

[axmls]

You have Newton's law defining the relationship between the force and the acceleration. You also have the velocity as a function of time. Now you need the acceleration. And you can plug that in for the force.

 

[deblimp]

No we do not have velocity as a function of time, we have it as a function of space. Therefore we can't just differentiate and get the accel.

 

[insightful]

Usually, these problems make use of the chain rule of differentiation.

 

[insightful]

Is "a" acceleration or just a constant in the equation?

 

[TheCanadian]

Homework Statement

The speed of a particle of mass m varies with space as v(x) =ax^-n
v(x=0)=0 at t=0.
Find F(x).

Homework Equations

F=ma=m dv/dt

The Attempt at a Solution

I am not really sure where to start from. Would x(t) or f(t) be relevant?

Try rearranging dv/dt