displacement and velocity

[ssh18]

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So, in TPR book it talks about how acceleration changes if either the velocity's speed or direction changes. This is also true for displacement right? If the magnitude or direction of the displacement changes then the velocity changes?

 

[RSAgator]

It is possible to have a CONSTANT acceleration AND have velocity change direction. You have a velocity of +10m/s and acceleration = -5m/s. Your velocity's direction will change even though your acceleration isn't changing. It is also possible to have velocity changing with a constant acceleration. For velocity to change, you simply need to have some acceleration, not a change in acceleration.

it's more appropriate to think of it as VELOCITY changes with acceleration than acceleration changes with velocity. After all, the definition of acceleration is the change in velocity.

For displacement, if you have any velocity then your displacement will change. Velocity is defined as the change in displacement/change in time. Thus if velocity is 0, change in displacement is 0. If velocity is some number other than 0, there is some change in displacement as time changes.

 

[TheBoondocks]

So, in TPR book it talks about how acceleration changes if either the velocity's speed or direction changes. This is also true for displacement right? If the magnitude or direction of the displacement changes then the velocity changes?

it is not true for displacement. What if you're moving in a straight line at constant velocity? Your displacement is changing, but your velocity isn't. As a result you're not accelerating. Just think about it in terms of acceleration. something accelerates if the magnitude of its velocity is changing or if it's changing direction (ie a circle). But it's true that if the displacement of an object changes direction then velocity changes since it's a vector.

 

[ssh18]

I'm a bit confused. How can velocity change (in either magnitude or direction) while the acceleration remains constant. If there is a change in velocity, doesn't that mean that the object's acceleration changes? or is it that a change in velocity only means the object is simply accelerating (and the value can be constant). Also, if only the direction changes then the magnitude of the acceleration is the same but is the direction change always reflected by a change in the sign for acceleration?

 

[BlackSails]

I'm a bit confused. How can velocity change (in either magnitude or direction) while the acceleration remains constant. If there is a change in velocity, doesn't that mean that the object's acceleration changes? or is it that a change in velocity only means the object is simply accelerating (and the value can be constant). Also, if only the direction changes then the magnitude of the acceleration is the same but is the direction change always reflected by a change in the sign for acceleration?

Lets say acceleration = 3. acceleration is constant. The speed is increasing by 3.

If there is a change in velocity, all it means is that acceleration is not equal to 0. If the direction the object is moving changes, the then object must have been accelerated.

Acceleration and velocity dont really have signs. They are vector quantities.

 

[RSAgator]

You need to go back and review this all.

You have 3 completely separate entities:

Displacement (x)
Velocity (x/t, or change in displacement/change in time)
Acceleration (x/t^2 or change in velocity/change in time)



Think of a person on a bungy chord. The start at some point which we will consider to be x = 0 (their initial displacement). We'll consider the down direction positive and the up direction negative.

They jump off a cliff and start to speed up. At this point they have a velocity downwards (positive). Since their velocity is increasing, they must have an acceleration that is in the same direction as the velocity so the acceleration must be downwards as well.

So to recap up to this point, a man jumps off a cliff. His velocity is positive and his velocity is increasing so his acceleration is in the same direction as velocity (positive as well). His displacement is also positive at this point because his velocity has caused him to move into the positive direction.

Now lets say after a certain point the bungy rope begins to pull him back up. We'll assume the bungy pulls him up at a constant acceleration of say -10m/s^2. His acceleration is negative so his velocity begins to slow down. However his velocity remains positive even though it is decreasing, and his displacement continues to increase (due to this positive velocity). Now since his acceleration is decreasing his velocity (because it acts in the opposite direction) his velocity is eventually going to reach 0. The acceleration still exists though so at this point his velocity will now become negative and start to become more negative and he will start moving back up (in the negative direction). His displacement will now begin to decrease because his velocity is in the up direction now.

This illustrates a lot of points:

Firstly while he is going downwards his acceleration is constant and his velocity is increasing.

Secondly when acceleration changes direction his acceleration becomes a different number, but it is still a constant. His velocity now decreases and eventually changes direction. At this point it begins to become more negative.

Hopefully you can understand some of that. I need to run.