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
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.
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
3 m/s - 1 m/s (the change in velocity)
---------------- = 1 m/s/s or 1 m/s^2
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
Jason (and Tom)
(republished on 07/11/06)