An object with mass m start its journey on x-axis at point (-l,0) with velocity v.
The object feels force which depends on the object's distance to origin.
After T second it reaches the origin. What is T?
The Attempt at a Solution
1: dx/dt = v(t)
2: dt = dx/v(t) [from 1]
3: dv/dt = a(t) = (-k/m) * x(t)
4: dt = m * dv/(-k * x(t)) [from 3]
5: v(t) * dv = (-k/m) * x(t) * dx [put 2 to 3]
6: integrating both sides of 5 and putting the values x=0 and the velocity at the origin (which can be calculated by the energy change with integrating f(x) dx from -l to zero) gives the relation between x and v.
7: Putting x in terms of v (found in 6) to 4 and integrating right side from initial velocity to velocity at the origin gives a time (dt at the left side).
But i am not sure about the answer. Any ideas will be great.