Understanding Acceleration: Exploring Velocity and Time

In summary, after reading about acceleration, the definition is change in velocity over a change in time. Velocity is the derivative of displacement, and acceleration is the derivative of velocity (and the second derivative of displacement). Derivatives are important when dealing with vectors, and can be explained with the concept of components. Linear acceleration is just a simple way of stating that acceleration is increasing speed over time.
  • #1
oldspice1212
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Hi guys, I've been having a pretty hard time understanding exactly what acceleration is, the definitions I usually see are always different, so from what I've read, I know acceleration is a vector quantity and the definition is basically change in velocity?
So if let's say a car is going 45 km/h east, and it changes its route to and speed (magnitude) to 35 km/h west, that would be change in acceleration right? Or do you have to account in the time as well, acceleration = velocity / time?
I may be over thinking this concept, but would be nice if someone can really clarify this for me, thanks again, huge fan of the physics forums.
 
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  • #2
oldspice1212 said:
Hi guys, I've been having a pretty hard time understanding exactly what acceleration is, the definitions I usually see are always different, so from what I've read, I know acceleration is a vector quantity and the definition is basically change in velocity?
No. It's change in velocity over a change in time. :wink:

oldspice1212 said:
So if let's say a car is going 45 km/h east, and it changes its route to and speed (magnitude) to 35 km/h west, that would be change in acceleration right? Or do you have to account in the time as well, acceleration = velocity / time?
I may be over thinking this concept, but would be nice if someone can really clarify this for me, thanks again, huge fan of the physics forums.
That would be a change in velocity. Not a change in acceleration.

What do you know about calculus? It's easy to explain if you know derivatives.
 
  • #3
Ah right change in velocity over time lol. I've taken calculus one, so yes I know about derivatives and such :p.
 
  • #4
oldspice1212 said:
Hi guys, I've been having a pretty hard time understanding exactly what acceleration is, the definitions I usually see are always different, so from what I've read, I know acceleration is a vector quantity and the definition is basically change in velocity?

This is essentially correct. To make it fully correct, say the rate of change in velocity. Rate implies that the "change" is divided by the time over which the "change" happens.

Just like velocity itself is the rate of change in displacement.

Mathematically, these "rate of change" things are known as "derivatives". Velocity is the derivative of displacement, and acceleration is the derivative of velocity (and the second derivative of displacement).

So if let's say a car is going 45 km/h east, and it changes its route to and speed (magnitude) to 35 km/h west, that would be change in acceleration right?

Change in velocity. It is -80 km/h. Note the minus sign, I assume that the eastern direction is positive.

Or do you have to account in the time as well, acceleration = velocity / time?

Not exactly. You do not need just time, you need the time it took for the change to occur. In your example, you did not give that time. If it took the car 20 seconds to undergo that change (say, by going through a roundabout), then the rate of change in velocity is (80 km/h) / (20 s) = 1.1 m/s2.
 
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  • #5
oldspice1212 said:
Ah right change in velocity over time lol. I've taken calculus one, so yes I know about derivatives and such :p.
Alright. That's good. Then, I'll introduce you to a new concept.

Since we can write a vector, let's say ##\vec{x}=\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}##, as a sum of the form ##\vec{x}=x_1\begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}+x_2\begin{bmatrix}0 \\ 1 \\ 0\end{bmatrix}+x_3\begin{bmatrix}0 \\ 0 \\ 1\end{bmatrix}##, we can say that vectors are differentiated by components. That is, ##\frac{d\vec{x}}{dt}=\frac{d}{dt}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}=\begin{bmatrix}\frac{dx_1}{dt} \\ \frac{dx_2}{dt} \\ \frac{dx_3}{dt}\end{bmatrix}##. This is the definition of the derivative of a vector (in Euclidean space) with respect to a scalar.

Thus, if we call ##\vec{x}## our displacement vector, then ##\vec{v}=\frac{d\vec{x}}{dt}## is the velocity vector and ##\vec{a}=\frac{d^2\vec{x}}{dt^2}## is the acceleration vector.
 
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  • #6
@Voko
Thanks Voko, I remember how the concept of derivatives relates to acceleration and other physics quantities now, your definitions were very helpful.

@Mandelbroth
I see somewhat of what you're saying, but at other places I feel lost lol, I'll have to fresh up on my linear algebra I think to fully understand the acceleration vector as you presented it. It is very much appreciated though, thank you!

Thanks guys!
 
  • #7
I'll put it in layman's terms.

You're traveling on a cycle.
You're speed after 1 second in 5 seconds is
0 second- 0 m/s
1 second- 2 m/s
2 seconds - 4 m/s
3 seconds - 6 m/s
4 seconds -8 m/s
5 seconds - 10 m/s

So what is happening is, you are increasing your speed by 2 m/s after every second. This makes your acceleration 2m/s/s or 2m/s^s.

This is just linear acceleration. For direction change, vector diagrams aer necessary.
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

2. How is acceleration different from velocity?

Velocity is the rate at which an object's position changes over time, while acceleration is the rate at which an object's velocity changes over time. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much an object's speed or direction is changing.

3. How is acceleration measured?

Acceleration is typically measured in meters per second squared (m/s^2). This means that for every second an object is in motion, its velocity changes by that amount. For example, if an object's acceleration is 5 m/s^2, its velocity will increase by 5 meters per second every second.

4. What factors affect acceleration?

The main factor that affects acceleration is the amount of force acting on an object. The greater the force, the greater the acceleration. Other factors that can affect acceleration include the mass and shape of the object, as well as external factors such as friction and air resistance.

5. How can we use the equation for acceleration to solve problems?

The equation for acceleration is a = (vf - vi) / t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval. This equation can be used to calculate any of these variables if the other three are known. It is also useful for solving problems involving motion, such as determining the distance traveled by an object or the time it takes to reach a certain velocity.

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