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### Course: AP®︎/College Physics 1>Unit 1

Lesson 1: Position, acceleration, and velocity

# Calculating average velocity or speed

Although speed and velocity are often words used interchangeably, in physics, they are distinct concepts. Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt. Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (Δt), represented by the equation r = d/Δt. Created by Sal Khan.

## Want to join the conversation?

• what is the difference between speed and velocity?
• There is not that much of a difference, but there are a few very important but subtle ones.

1) Speed is a scalar (only magnitude) and Velocity is a vector (magnitude AND DIRECTION)

2) You will only have a positive speed, but velocity can be negative if you are moving in the negative direction (which depends on the coordinate axes you use)

3) Speed basically tells how fast something is moving, but velocity tells us the rate which an object changes position (delta x divided by delta t, or dx/dt if you know derivatives)

Check out this site: http://www.physicsclassroom.com/class/1dkin/u1l1d.cfm
It should help with your question if I don't.

Hope it helps :)
• could it be that we use S for displacement because of the Latin word spatium which means distance?
• Seems highly probable.
• What is the actual purpose of having a velocity ? Like in real life problems we deal with speed, I am moving with a speed of this and If I reach to the same point where I started from and If someone says you have an avg velocity is zero, It sound so weird, I mean I spent a lot of energy and time from travelling from one point to other and I find my vel is zero and speed is something. In short What was the purpose to bring the velocity concept in physics?
• Thats a nice question....

In a way, you are asking the question "what is the point in vectors...?"
vectors contain more information than scalars and the relative directions velocity become very important when dealing with the next level (or derivative) acceleration. Acceleration is the change in velocity over the time taken to make the change. This will, then, be influenced by the angle between the final and initial velocities.

Kinetic theory:
when we consider the average velocity of particles in a gas, we find that it, too , is zero. whereas the mean kinetic energy of all the particles in the gas is non-zero because it is related to the average velocity (squared).

hope that helps
• If the problem indicated that Shantanu traveled 5 km north and then 4 km south, would the average velocity be 1 km/hour or 9 km/hour. i.e would you use the distance traveled or displacement?
• You would have to use the distance traveled. For example, if you were stopped by a police officer, going 70 mph (average) in a 55 mph zone, he/she would not let you get away if you just reversed quickly, and then said that your average speed now is 55 mph.
• is there a difference between magnitude and measurement?
• Magnitude is the relative size or extent but measurement is the numerical amount.
• The letter "s" is commonly used to denote displacement because of its historical origins. In physics, the symbol "s" for displacement comes from the Latin word "spatium," which means space
• at , why does Sal say the average speed is 5 kilometers per hour to the north? Shouldn't it just be 5 kilometers per hour because it's the same speed if you are going south or east or west?
• If you were referring to speed, you would be right, but since we are dealing with velocity, a *vector,* which in a previous video he explained that a vector has a position/size and a *direction.* Speed is a schalar, which he is not using, which does not have a direction.
• At , what is constant velocity?
• Constant velocity here means that his velocity was not changing so neither his speed nor his direction would change, everything would remain constant.
• i can't understand what is the point of velocity? like for example if i go jogging i would want to know what my average speed is..why would i want to know the velocity?
• Hi Viveka,

You don't know this yet but you have just asked a very important question. A question that will change the way you view the world and how you look at mathematics.

Suppose you are the driver of a race car. Now suppose you modify this car with a rocket assist. I think you will agree that the rocket assisted car will have a greater acceleration.

But wait, what is acceleration? Acceleration is defined as the rate of change in velocity. In the rocket assisted car the velocity is changing very fast. You will be "pushed" forcefully back into the seat as you drive this car. Stated another way you will go from 0 to 60 very quickly.

I could go on but I think you see the point. Without the concept of velocity you can't talk about more interesting things like acceleration.

Know that there is an entire field of mathematics devoted to the study of things in motion.

I wish you success in calculus.

Regards,

APD