Question corncerning acceleration and velocity

[seasnake]

I'm defining acceleration as present speed minus previous speed within the confines of a spreadsheet. The problem with this is that the speed between the current and the previous is constantly uniform, that is the average speed of the interval is 0.5(S-Sx)+Sx. But I do not know if the object sped up or and slowed down several times, or if the object went faster in the first portion and slower in the latter. I assume that if the speed varied during the interval then the 0.5 figure would adjust to balance the equation of 0.5(S-Sx) = (new weight)(S-Sx).

Given the above, I would like to know if the interval's velocity would be equal to (S-Sx)/(new weight) + Sx.

My understanding of the difference between speed and velocity is that speed is measured from one interval to the next ignoring what occurs inbetween the measurements and velocity accounts for both speed and anything that has been lost during the speed interval.

I would like to know if my understanding is correct, and if not, then how it is not.

I also need to know when expanding squares such as, (x+y)^2 to x^2 + 2xy + y^2 if the 2 in the 2xy term should be expressed by another variable when dealing with velocity (1/0.5 = 2, but has intra-interval changes been ignored?).

 

[diazona]

Here's the scoop: velocity is the derivative of position. That is, it's the change in position over an infinitesimally small time, divided by that infinitesimal time interval. In practice, we can't measure infinitesimal time intervals or infinitesimal changes in position, so we settle for computing the average velocity over very short time intervals. If those small time intervals are short enough that the true velocity doesn't change much over the course of one interval, you get a close approximation of the true velocity.

Speed is just the magnitude (or absolute value) of velocity. For instance, if you have one ball moving at 2 m/s to the right and another moving at 2 m/s to the left, they have opposite velocities but the same speed.

I'm not sure what you're talking about with respect to expanding squares... (x+y)^2 = x^2 + 2xy + y^2, period.

 

[tiny-tim]

My understanding of the difference between speed and velocity is that speed is measured from one interval to the next ignoring what occurs inbetween the measurements and velocity accounts for both speed and anything that has been lost during the speed interval.

I would like to know if my understanding is correct, and if not, then how it is not.

Hi seasnake!

No … that's the difference between average speed (over an interval) and instantaneous speed …

speed and velocity (in a constant direction, which is what you're using) are the same

(technically, velocity is a vector, and speed is the magnitude of velocity )

I also need to know when expanding squares such as, (x+y)^2 to x^2 + 2xy + y^2 if the 2 in the 2xy term should be expressed by another variable when dealing with velocity (1/0.5 = 2, but has intra-interval changes been ignored?).

Sorry, not following you.