A particle moving in a straight line experiences a force numerically equal to 2/x2 per unit mass towards the origin. Find the time taken to reach the origin if the particle starts at rest 4 units from the origin.
I have been able to arrive at an equation:
a(x) = 2/x2 (as force per unit mass, I am assuming mass to be 1 unit)
a(x) = dv/dt = dv/dx . dx/dt = v dv/dx (chain rule)
Hence, v dv = (2/x2) dx
v2/2 = (-2/x2) + c
v2 = (-4/x) + C
but at x=4, v=0
Hence, C = 1
My final equation: v2 = (-4/x) +1
But from the looks of it trying to find x(t) and then setting to zero seems too difficult. How else can you solve this? The answer is 2 pi seconds
I have been able to arrive at an equation:
a(x) = 2/x2 (as force per unit mass, I am assuming mass to be 1 unit)
a(x) = dv/dt = dv/dx . dx/dt = v dv/dx (chain rule)
Hence, v dv = (2/x2) dx
v2/2 = (-2/x2) + c
v2 = (-4/x) + C
but at x=4, v=0
Hence, C = 1
My final equation: v2 = (-4/x) +1
But from the looks of it trying to find x(t) and then setting to zero seems too difficult. How else can you solve this? The answer is 2 pi seconds