Force given velocity as function of space.

AI Thread Summary
The problem involves finding the force F(x) for a particle of mass m with velocity defined as v(x) = ax^-n, where v(0) = 0 at t = 0. The relationship between force and acceleration is given by F = ma = m dv/dt. Since velocity is expressed as a function of space rather than time, direct differentiation to find acceleration is not possible. The chain rule of differentiation is suggested as a necessary approach to relate the variables correctly. Understanding whether "a" represents acceleration or a constant is also crucial for solving the problem.
deblimp
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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?
 
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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.
 
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.
 
Usually, these problems make use of the chain rule of differentiation.
 
Is "a" acceleration or just a constant in the equation?
 
deblimp said:

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
 

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