Question

An object of mass m moves in one dimension with velocity given by v a/x for a a constant. Find the force on the object as a function of position and the position time. To find the force, you may use either Newton's 2nd law or energy conservation. Assume that the object is initially at the origin.

Answer 1

Answer:

$F = -m\frac{a^2}{x^3}$

Explanation:

As we know that velocity as a function of position is given as

$v = \frac{a}{x}$

now in order to find the acceleration we can use that rate of change in velocity is known as acceleration

So we will have

$a = \frac{dv}{dt}$

$a = \frac{d}{dt}(\frac{a}{x})$

$a = -\frac{a}{x^2}\frac{dx}{dt}$

$a = - \frac{a^2}{x^3}$

Now by Newton's 2nd law we have

$F = ma$

$F = -m\frac{a^2}{x^3}$