## Ask Professor Puzzler

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A visitor from Nigeria asks, "What is the different between aceleretion and velocity?"

Acceleration and velocity are two quantities that we deal with in the field of Physics. They are related, but quite different concepts.

Let's start by talking about something acceleration and and velocity have in common. They are both *vectors*. Back when I was in school, students never heard of vectors until they hit high school Physics class, but nowadays, most kids learn what a vector is much earlier than that. And they don't learn it at school. They learn it while watching the movie "Despicable Me."

The character Vector announces to Gru that his name is vector because, "I commit crimes with both direction and magnitude."

A vector contains two pieces of information - a size (magnitude) and a direction. Velocity and acceleration are both vectors.

Another way in which velocity and acceleration are similar: they both relate to the motion of an object.

Velocity is a way of defining the motion of an object. It can be described as a speed and direction of motion. For example, a car is traveling at 60 mph East. 60 mph is the magnitude, and east is the direction. I'm in an elevator that is going down to the first floor at a speed of 5 m/s. 5 m/s is the magnitude, down is the direction.

So what is acceleration? Acceleration is the rate at which the velocity is changing. It is also a vector, so it also has a magnitude and a direction. For example, In the elevator example above, if the elevator had an acceleration of 1 m/s^{2}*up*, that would mean that every second, the speed of the object is decreasing by 1 m/s. So after one second, the elevator would be traveling at 4 m/s. After two seconds, it would be traveling at 3 m/s. And after five seconds, it would be standing still.

On the other hand, if the elevator had an acceleration of 1 m/s^{2} *down*, the elevator would be speeding up.

If the cable on the elevator broke, it would have a *downward *acceleration of 9.8 m/s^{2}. As you might imagine, that would be downright terrifying. After one second, the elevator would have a velocity of 14.8 m/s down. After two seconds, 24.6 m/s down, which is about 55 mph down. Obviously, there's a good reason to be concerned if the cable breaks!

If the elevator had an acceleration of 1 m/s^{2} *west*, that would mean that as the elevator is dropping, it's also picking up speed in a horizontal direction, which - I suppose - means it's crashing through the side of the elevator shaft!

Any time the velocity is changing, you have an acceleration. If the velocity is not changing, the acceleration is zero.

When I'm teaching acceleration to my physics class, I always ask them how many accelerators their car has. They usually respond by saying, "The gas pedal." I tell them that's not the only one. They ponder for awhile, and then realize that the brake is also an accelerator; it gives an acceleration in the opposite direction of the motion. I tell them they're still not done, and remind them that velocity is a *vector*, which includes a *direction*, and that acceleration is the rate of change in velocity. Eventually, someone realizes that the steering wheel is also an accelerator, because it changes the direction of the car.