# Question corncerning acceleration and velocity

• seasnake
In summary, the difference between speed and velocity is that speed is measured over a certain interval of time while velocity takes into account the direction and any changes that occur during that interval. The average velocity can be approximated by calculating the average speed over very short time intervals. Speed and velocity are essentially the same in a constant direction. The expansion of squares, such as (x+y)^2, does not involve any variables when dealing with 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?).

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.

seasnake said:
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. ## What is the difference between acceleration and velocity?

Acceleration is the rate of change of velocity with respect to time, while velocity is the rate of change of displacement with respect to time. In other words, acceleration is how much an object's velocity changes in a given time period, while velocity is the speed and direction of an object's motion.

## How can I calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (v2-v1)/t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

## What is the unit for acceleration?

The unit for acceleration is meters per second squared (m/s^2). This means that for every second an object is accelerating, its velocity is changing by m/s.

## How are acceleration and velocity related?

Acceleration and velocity are related in that acceleration is the rate of change of velocity. This means that changes in acceleration will cause changes in velocity, and vice versa.

## What is the difference between positive and negative acceleration?

Positive acceleration occurs when an object's velocity is increasing, while negative acceleration (also known as deceleration) occurs when an object's velocity is decreasing. Positive acceleration is often associated with speeding up, while negative acceleration is often associated with slowing down.