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### Course: Physics library>Unit 1

Lesson 3: Acceleration

# Acceleration

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction. Created by Sal Khan.

## Want to join the conversation?

• how do u find momentum
• Momentum is found by multiplying the mass which is moving by its velocity. Momentum is typically represented by the variable "p", so the equation for finding momentum would be "p=mv".
• Ok so I just wanna make sure I understand this correctly: So the reason seconds is squared is because it is seconds PER second, right?
• I think you get the point, but it may be easy to be misinterpret. If I were to try to figure out the number of units of time per another unit of time. It might be difficult to get from how it is said, exactly, but it's because you are taking velocity (which is already in meters per second) and dividing it further by another unit of seconds, meaning you effectively have ((m/s)/s).
• so speed without direction is a scalar quality and velocity is speed with direction making it a vector quality, right?
• yes as long as a number assosiated with how fast an object is moveing has a dirction it is a vector quality otherwise its a scaler quality
• As I know lots about cars, I know that accelerating in the beginning is easier than when you go higher because engine needs to maintain the old speed + add new speed (accelerate)......I am assuming the 20mph/second^2 to be the average of the three seconds of acceleration. For example, say that the car accelerated up to 23mph in the first second, 21 mph in the 2nd second, and 19mph in the 3rd second. It wouldn't have been exactly 20, 20, 20......So my question is, is there any way we can find the three possible exact values of each second of acceleration according to the info I have just given using physics?
• You're technically referring to average values for each second as well. From the initial set of information described, it is not possible to get back to more detailed information about each second or the more desirable instantaneous acceleration (the slope of the velocity graph at a particular point) from which it's possible to get any other information about the average acceleration overall or over any sub-period within said range (see integral calculus for details on how).

Short of it, no. Averaging a set of data hides completely the details interior to it so you can't reverse it.
• What about deceleration? what's the definition and how do you calculate it? is it any different from calculating acceleration? except for maybe some negative values?
• Deceleration is just acceleration, where the acceleration vector is pointing in the opposite direction in respect to the velocity vector. Usually in physics we only say acceleration but give a direction (because it is a vector).
For example: if you are moving at 3m/s to the right and accelerating at -1m/s/s, then you are "decelerating" by 1 m/s every second. After 3 seconds you will have decelerated to 0 m/s.

Do you understand? If not commment and we can continue the conversation.
• I watched all the videos in this chapter but couldn’t find about the formula xf=xi+vit+1/2at^2 which was appeared at the position acceleration and velocity questions. Can I ask the explanation of that formula?
• It is an equation to calculate the Final Position Xf when you have the Initial Position Xi, Initial Velocity Vi, Acceleration Rate A and the amount of time from the Initial to Final position T.
(1 vote)
• what is a porsche?
• A Porsche is a make of German sports car.
• At , how did he cancel out the hour from the denominator ?
• To be honest, I find this explanation is confusing since it mixes incomplete explanations about acceleration and unit conversion.

Your question is related to the second topic (unit conversion) and is not explained sufficiently here, I think. For some reason the lecturer is trying to put the final result in miles/second/second. Do not ask me why exactly, I would stick with miles/hour/second which are valid units, or go to meter/second/second (International units).

Anyway, you have miles/hour/second and you want to change then hours to seconds.
The way to do this is: You can always multiply by a fraction equal to 1 (which would change nothing). So your trivial multiplying factor would be 1 hour / 1 hour but since 3600 seconds equals to 1 hour, this can be written as well as 1 hour / 3600 which is a convenient conversion factor from hours to seconds. Then hour units cancel out when multiplying and you got your result in seconds.

You may consider instead the reverse fraction: 3600 seconds / 1 hour, but you can discard this since it would not cancel out.

This is general procedure for any units conversion and can be applied multiple times until converting to convenient units.
• I'm trying to understand what all of these kinematic formulas mean. So playing around with some graphs, I came up with a question. I am sure the answer is simple, but I don't yet know it.
Imagine that I start with a velocity of 0 and accelerate for four seconds (constant), and have a final velocity of 3 m/s.
Therefore, constant acceleration would = 3/4 m/s². The magnitude of the graph over this time period would = √3²+4².
What does this magnitude represent, and how would it be used?