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# 2011 Calculus AB free response #1a

Determining whether speed is increasing. Difference between speed and acceleration. Created by Sal Khan.

## Want to join the conversation?

• As someone who isn't familiar with what AP/AB placement is, could someone explain it briefly so I can think of a local comparison?
• AP stands for Advanced Placement, while AB could stand for Calculus AB which represents the first part of the Calculus cumulative course. The AP exam includes an AP Calculus AB exam, where the AB stands quite simply for the 1st section of Calculus taught according to the AP standards.
• At : Why is the speed increasing?
• So unlike velocity, speed is a scalar quantity. That is, it only has a magnitude (not direction). So, at when Sal references the particle's speed and says that it is "increasing", he's doing so with the knowledge that the particle's velocity vector is moving in the negative direction. Try picking a negative number and moving in the negative direction, the magnitude (or absolute value) of the number increases, doesn't it? It is confusing, but this is all he's saying here.
I hope this helps.
• Whatever happened to the video for parts b, c, & d??
• What are the applications of Calculus?
• Calculus has many applications. It has so many applications that I cannot begin to describe them to you. Calculus pervades math (obviously) and the sciences. Even a scientific discipline like biology can use calculus to study rates of diffusion etc. It also has very important implications for the study of physics (which was kind of why it was invented) and engineering. Whenever you play a video game that involves laws of physics (like gravity, magnets...some sort of attractive forces) you can bet that there is calculus involved. The machine may not be doing integrals like you can, but it makes numerical calculations based on the same principles of Riemann sums that you have learned.
The possibilites are limitless!
• At around : What is the magnitude?
• Remember, velocity is a vector quantity, so it has both direction and magnitude. In the example at , the particle said to be moving in the negative direction and with a magnitude of 5.
• Do I use radians or degrees for this problem?
• You should never use degrees in calculus. It is always radians unless for some bizarre reason some problem asks for degrees. Even if you do use degrees, you have to effectively convert them into radians to do the math.
• I'm confused by everything concerning the velocity here. Can anyone re - explain it to me, please?
• Velocity is like having a line and moving on it
moving right is positive
moving left is negative
Your speed is how fast you are moving
Your velocity basicaly tells you where you are going to be in a certain amount of time
It tells you how far and in what direction
If you say that your velocity is -15 fps then your are going left at a speed of 15 fps.
While Saying that your velocity is 15 fps means that you are going right at at a speed of 15 fps.
Same speed, different direction, different velocity.
• Correct me if I am wrong:

If acceleration is positive and velocity is positive, then velocity is increasing and speed is increasing.

If acceleration is positive and velocity is negative, then velocity is increasing but speed is decreasing.

If acceleration is negative and velocity is positive, then velocity is decreasing and speed is decreasing.

If acceleration is negative and velocity is negative, then velocity is decreasing but speed is increasing.
• At around , what you're saying is that speed is equal to the absolute value of the velocity?