Position, Velocity, and Acceleration
All exact science is dominated by the idea of approximation.
Editors Note: This page is heavy on mathematics so these sections are suggested
for readers who have taken at least algebra and geometry.
- Bertrand Russell (1872-1970)
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.
I hope that you noticed the phrase "rate something changes over time." That
phrase can be written in mathematical symbols.
- 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.
Velocity = dx/dt
Acceleration = dv/dt
What does dx, dv, and dt refer to?
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
- dx means the change in x (position)
- dv means the change in v (velocity)
- dt means the change in t (time)