Question

If a single constant force acts on an object that moves on a straight line, the object's velocity is a linear function of time. The equation gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position?

Answer 1

F = -kmv

Step-by-step explanation:

The computation is shown below:

As we know that

a = acceleration

v = velocity

Given that

v = v_i - kx

Based on the above information

`(dv)/(dt) = (dv_i)/(dt) = k (dx)/(dt) = 0 - kv = -kv`

a = -kv ..................(i)

Now multiply both sides of an equation

BY mass of the object

ma = -kmv

F = -kmv

So if there is no other external forces so the force is on object i.e.

F = -kmv