Non-uniform acceleration equation

[candycooke]

I need to know the non-uniform acceleration equation to determine final position given:
initial position
initial velocity
initial acceleration
jerk
time

I know that the equation with uniform acceleration is:
x(f) = x(i) + v(i)t + (1/2)at^2

I think the equation I'm looking for is the following, but I'm not exactly certain:
x(f) = x(i) + v(i)t + (1/2)at^2 + (1/6)jt^3

Thanks

 

[Gib Z]

Assuming that your jerk is constant, and that "a" in your equation is the initial acceleration [so by your notation, a(i)], then yes, you have the correct equation . =]

 

[thomate1]

I can confirm that the equation you are looking for is correct. The non-uniform acceleration equation takes into account not only the initial position, velocity, and acceleration, but also the jerk (the change in acceleration over time). This equation is known as the "polynomial motion equation" and is commonly used to calculate the final position of an object undergoing non-uniform acceleration. By including the jerk term, it allows for a more accurate representation of the object's motion over time. I hope this helps in your calculations!