Physics - Kinematics Notes
Velocity

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Speed is Inadequate to Describe Motion

Suppose a car leaves Chicago and travels for 4 hours with an average speed of 50 miles/hour. Where will it be at the end of this time?

Who knows? The car could be 200 miles (= 50 mi/hr x 4 hr) north of Chicago, it could be 200 miles west - or any other direction. It could even be back in Chicago (if it went 2 hours west, then 2 hours east, for instance)! It could be anywhere within a 200 mile radius of Chicago. That is not a very precise description of the car's motion!

Clearly, speed is not adequate to describe the motion of an object. You need to know its speed and direction. Velocity is the kinematics concept that describes an objects speed and its direction.

Average Velocity

The average velocity of an object is its average speed and its direction.

Instantaneous Velocity

The instantaneous velocity of an object is its instantaneous speed and its current direction.

Note that when a physicist says "velocity", she is referring to instantaneous velocity - if you are talking about average velocity, you have to say "average velocity".

Specifying the Direction of a Velocity

If someone asks for the velocity of an object, they want 2 pieces of information - its speed and direction. There are several common methods for specifying 2-dimensional velocities; compass directions (0^o is north, 90^o is east, 180^o is south, 270^o is west), the "degrees from direction" method (30^o east of north, for instance). For situations that don't lend themselves to compass directions, specify an angle from the horizontal or vertical, etc.

For one-dimensional motion, the job is simpler. Velocities in the positive direction are positive. Velocities in the negative direction are negative.

Don't jump to conclusions here. The diagram above does not mean that velocities to the left are always negative! We customarily make this direction negative, but there is no binding reason for doing so. In a problem involving vertical motion, the upward direction may be considered to be either positive or negative. The point is, whatever direction you consider to be positive in a situation, velocities that way are positive, velocities the other way are negative.

Changes in Velocity

It is important that you be able to recognize when the velocity of an object is changing. Since velocity is speed and direction, the velocity of an object changes if:

1. it speeds up.
2. it slows down.
3. it changes direction.

Note that the velocity of an object can change, even if its speed remains constant. For instance, when a car is going around a curve (like an entrance ramp on an interstate), it is accelerating - even if the speed of the car stays the same. Velocity changes when either speed or direction changes.

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Practice Quiz on Velocity: