Stadium Dugout Announcer's Booth Batting Cage Bullpen Behind the Plate

## Position, Velocity, and Acceleration

All exact science is dominated by the idea of approximation.
- Bertrand Russell (1872-1970)
Editors Note: This page is heavy on mathematics so these sections are suggested for readers who have taken at least algebra and geometry.

When we derive equations, the terms position, velocity, and acceleration are often used. So what are these terms, and how do they help us in deriving equations? We will briefly go over them, but if you wish for a full understanding we suggest that you should look them up in a good physics or mathematics book.

• Position is the position. Fairly obvious, position tells the current location of an object.
• Velocity is the rate the position changes over time. It is commonly referred to as speed and many people mistakenly interchange the words velocity and speed as if they mean the same. They are not. Velocity is a vector while speed is the scalar of the vector. What is a vector and a scalar? Vector can be thought of as an arrow with specific direction and length. Scalar is the length portion of the vector. For example, a velocity could be 70 miles per hour to the north, while its corresponding speed would be 70 mile per hour.
• Acceleration is the rate the velocity changes over time.
I hope that you noticed the phrase "rate something changes over time." That phrase can be written in mathematical symbols.
Velocity = dx/dt
Acceleration = dv/dt
What does dx, dv, and dt refer to?
• dx means the change in x (position)
• dv means the change in v (velocity)
• dt means the change in t (time)
So this is all great but what does all this junk have to do with deriving equations you ask. Well, in most physics problems you know one or more parts of the equation. In the case of finding the equation of the range of the baseball, we already knew dy (change in height) which was 0, and with that knowledge we were able to simplify the equation and solve the range of the baseball.