Ryan95 said:Honestly, I am totally lost on this. I've written acceleration as v(dv/dt) which gave me mv(dv/dx)=Kx and then tried separating variables to integrate, but once I do that, I'm totally lost as I end up with m(v2/2)=K(x2/2).
drvrm said:i wonder how one can write acceleration as v..dv/dt as we know it as rate of change of velocity with time.. may be a typo.
now dv/dt can be expressed as d/dxof v multiplied by dx/dt .
i think you should proceed with the analysis as per the rule of integration and have initial conditions at t=0 and try to find x as a function of t. as one normally does with constant forces.
x(t) is the displacement of an object at time t.
x(t) is directly proportional to the Kx force and inversely proportional to the mass m. This means that as the Kx force increases, the displacement x(t) also increases, while increasing the mass m decreases the displacement x(t).
Yes, x(t) can be negative if the object is moving in the opposite direction of the Kx force.
You can use the equation x(t) = (Kx force/mass m) * t^2, where t is the time in seconds.
Yes, x(t) can also be affected by other forces such as friction and air resistance, as well as external factors like the object's initial velocity and angle of motion.