Speed and Velocity, the Identical Twins

[Raiden]

Alright. This is a simple question, but it does give me some problems. What's the difference between Speed and Velocity? They're basically the same things, at least in my mind. And it would be nice to truly know the difference so that I can use it to calculate stuff like displacement and acceleration.

 

[Janus]

Speed is just magnitude

velocity is magnitude and direction.

Thus an object's speed would be 5 mph, but its velocity might be 5 mph East.

If you have two cars, one driving west at 60 mph and the other driving East at 60 mph, they have the same speed but different velocities.

As far as acceleration goes, it is a change in velocity, which could mean a change of speed, direction, or both.

For example, an object traveling in a circle at a constant speed, is constantly changing direction and therefore is undergoing acceleration.

 

[HallsofIvy]

Another way of saying what Janus did: "velocity" is a vector quantity. "Speed" is the magnitude of the velocity vector.

In a very simple, one dimensional case, an object moving in the positive direction with speed 10 m/s would have velocity +10 m/s while one moving at the same speed in the negative direction would have velocity -10 m/s.

In two dimensions, if we take the positive x-axis pointing east and the positive y-axis north, then a car moving east at 60 mph would have velocity vector <60, 0> while one moving west at 60 mph would have velocity vector <-60,0>. Similarly, a car moving north at 60 mph would have velocity vector <0, 60> and a car moving south at 60 mph would have velocity vector <0,-60>.

A car moving north-east at 60 mph is a little harder. Its velocity vector is <60/&radic;(2), 60/&radic;(2)>.

The speed in every one of those examples is, of course, 60 mph.