# Q & A: Speed, Velocity, Acceleration, Oh my!

Q:
distinguish between speed,velocity and acceleration
- ansaar
karachi pakistandis
A:
Hi Ansaar,

Velocity is the change in position divided by the change in time. For instance:

If I travel in a straight line 5 meters away from you, and it takes me 5 seconds to do so, my velocity is:

`5 meters - 0 meters -------------------  = 1 meter/second 5 seconds `

If you've had a calculus course, the explanation is even more interesting. The velocity is the slope of the graph of position vs time, where position is a function of time.

Velocity is called a vector quantity, because both the direction and the magnitude (speed) are important. Speed is called a scalar quantity, because only magnitude (quickness) is important, direction isn't. Speed is the absolute value of velocity.

Example:

If I walk in a straight line 5 meters towards you, and it takes me 5 seconds, my velocity is -1 meter/second. It is negative not because I'm slowing down or stopping but because I am walking toward you, not away from you. I'm walking toward where I came from. My speed in this instance is 1 meter/second, since direction isn't a factor when finding speed. Velocity has three "components" because space is three-dimensional. North, East, and up are three mutually perpendicular directions. Velocity in the South direction is just negative velocity in the North direction; velocity in the West direction is negative East velocity, and down velocity is negative up velocity. Velocity in any other direction in between these can be expressed as a sum of velocities along the three main axes.

Acceleration is the change in velocity divided by the change in time.

If I start going 1 meter a second walking away from you but speed up and go 3 meters a second away from you, and it takes me 2 seconds to do so:

`3 m/s - 1 m/s   (the change in velocity) ---------------- = 1 m/s/s or 1 m/s^2 2 seconds `

Acceleration is given in meters/second^2. This makes sense if you consider that you're finding the meters per second PER second.

Calculus provides another interesting view of this puzzle. Acceleration is the first derivative of the velocity as a function of time or the second derivative of the position as a function of time. If you graph the acceleration of an object and find the area under the curve, that integral is the velocity.

Acceleration also has a magnitude and direction (although in this case we don't have separate words for the two). Acceleration can be expressed as having components along the main three directions in space, just like the velocity. One interesting property is that if the velocity changes direction but the speed remains constant, there is still acceleration.

Jason (and Tom)

(published on 10/22/2007)