(i'm "not" looking for coding help. i need help setting up the math.)
i'm writing a program for a physics class to find the velocity of an object across a random curve. where the only force acting on it is gravity (g).
the goal is to compare the found results from the kinematic equations. with the value found from conservation of energy.
i'm currently finding the instantaneous velocities at each point along the curve and summing the values. so basically this V^2 = 2*A*S. where A = sin(theta)*g , theta = arctan(dy/dx) , and S = the arc length. i sum the V^2s for each interval and take its root. this is giving the right answer.
how ever my professor wants me to use an equation that uses time as well. and this is the problem i don't have a clue how to do this. as i'm not sure how to determine the change in acceleration with respect to time across a fixed path (example a curve that looks like y=x^2).
i could be misunderstanding what he is requesting. however even if i am, if this is possible i would like to know how it's done.
i think this deals with jerk but i don't know how i would find a value to fit a fixed curve. i've looked for jerk examples and found some that have been helpful but none that deal with following a path along some surface.
as a side note i'm already defining my curves parametrically as it allowed me to get around the problem of "dx = 0". and just in case that turns out to be the way to solve this.
i thought i could numerically integrate (r = x +v*t+.5*a*t^2) by finding the instantaneous acceleration for each time interval and using it to find V and then the change in position. however i'm not always getting answers that make sense no mater the size of delta t.
thank you all for your help.