Calculating with constant acceleration
I am so confused as to what the light blue and light pink area are supposed to mean. Are we calculating
velocities from those to areas and dividing them by the time to generate an instantaneous velocity.
In the given examples, the area under the linear graphs could be calculated very easily and neatly. But in
case there are curves, how precise do our answers need to be?
Is the change in velocity over change in time only used to when acceleration is constant or can it be used
to calculate the acceleration at any interval?
What is the point of "moving" a constant and making it a variable?
Is there a way to figure out if the blue part and the pink part of the graph are equal using the graph rather
than using an equation?
What do we do if acceleration is not constant, by knowing that area under true velocity curve equals the
area under average velocity. In other words, Is it always true that area under true velocity curve equals
area under average velocity or does it change if the acceleration is not constant?
I'm a little confused about treating t2 as a variable. Why are we able to take a constant and treat it like a
variable?
If the velocity is constant, wouldn't the acceleration be zero and not just a constant. My reasoning is that
since acceleration is defined as change in velocity over time, wouldn't that mean that the numerator would
become zero and the acceleration become zero?
For constant acceleration, suppose we are not traveling along a straight line, and therefore will not be
able to use i-hat or j-hat. What will we use in place of them if we are considering an angle of motion?
What does "constant acceleration" mean in terms of changing position?
This really confused me. Could you explain it again in class
In what real-world biological context can acceleration be assumed to be constant?
What do you do when your acceleration is not a constant? Do you have to use a different equation?
Why don't we have to take the angles of motion into consideration when thinking about average velocity?
How does the equation change if the acceleration is not constant?
When it come to application, what circumstances would allow for constant acceleration? (application
being in a biological setting)?
With all these calculations and formulas, I see no units. Where does that come into play?
I'm still a little confused on the difference between average acceleration and instantaneous acceleration,
can you further explain the two?
If the equation for acceleration is the change in velocity over change in time, is the acceleration the
derivative of velocity?
If an object does go at an angle, would this impact the acceleration even if it is constant?
It wasn't clear why you would let a constant "wander around" and let it become a variable.
How is a constant acceleration represented by a position vs time graph? Can a position vs time graph
demonstrate a constant acceleration by converting from position to velocity to acceleration?
Will something ever be truly traveling at constant acceleration? In order to achieve constant acceleration,
the velocity must be changing at a constant rate too, but does that ever happen?
I don't understand this equation: ?x = <v>?t. Is it saying that the change in x is equal to velocity times the
change in time? If so, what does the change in x measure?
Is acceleration a vector? Meaning does it have a direction and magnitude?
What if you plugged in average velocity rearranged into the position equation? As here:
delta V=delta a x delta t
delta x= (delta a x delta t) x delta t
delta x =delta a delta t x delta t^2
Was the point of this reading to explain that you can rearrange the average velocity and average
acceleration equations like this?
delta V=delta x / delta t............delta x=delta V x delta t
delta a=delta V/ delta T.............delta v=delta a x delta t
What has constant acceleration other than gravity?
Since these equations all rely on the acceleration being constant, will the acceleration typically be
constant? Or is it more usual to encounter a non-constant acceleration?
Is acceleration expressed in m/s^2?
If we are calculating with constant acceleration, what is the point of of finding the average velocity if the
velocity changes at a constant rate for the interval? How would calculations such as finding average
velocity change if acceleration is not constant?
I am still a little change in velocity and the concept of acceleration.
How do you solve the equation to get v2 = v1 + a0 (t2 - t1)? a
Will the graph for velocity always be a straight line? If not, how do we solve for average velocity and
acceleration?
How does finding the acceleration change when the velocity doesn't change at a constant pace?
Since constant acceleration means the "velocity is either increasing or decreasing at uniform rate", can
the velocity be negative when decreasing or is the velocity expressed as a fraction when its decreasing?
What if the acceleration is not constant? How do we determine what the average velocity is?
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For a typical exam problem, would I be correct in assuming that we'd be using the formulas to sold for any
unknowns in the formula? Would we ever get a case where we'd be solving for multiple unknowns in one
equation?
With these equations calculating for average velocity, could we tweak the equation and calculate for the
average velocity at certain time intervals?
If we were to graph a constant acceleration vs time on a graph, do we can a horizontal line
Is acceleration speed?
How often is it that a real movement in space and time can be described when the acceleration is a
constant? Could you give me an example of when something is moving at a constant acceleration, in the
real world?
I don't understand what the point of treating t2 as a variable, and how it changes the equation?
Looking at the graphs, why is the constant line needed to determine average velocity? What does the
area under the curve tell us?
I do not seem to understand why you would not include the pink portion of the area under the curve? Why
do these different areas need to be equal?
We covered derivatives and integrals in calculus without much theoretical understanding of the topic. That
made it a lot more difficult to understand the concept, because it wasn't connected to any real-world
ideas, and I could only visualize it as an equation. Do you think our calculus requirement should be
replaced with a physics requirement?
Can acceleration be negative?
Can you give another example of when we should fix a variable at a constant value or make a constant a
variable?
Does the velocity and acceleration always relate to each, even in real world situations?
This equation, v(t) = v1 + a0 (t2 - t1), was given as a way to determine average velocity, can it also be
used to determine instantaneous velocity? Additionally can you provide an example of a problem in which
this equation can be used to find one or both?
What do you mean by letting a constant 'wander around'?
What is the constant line and how do we find it when figuring out the average velocity based on a graph?
Can we always change any constant into a variable in any equation?
How can you tell if the acceleration is constant when you only have average velocity?
Why is that the kinematic equations only apply under uniform motion?
What is another example in which a constant is changed to a variable to make an equation?
How would be solving for a final velocity with a constant acceleration? Wouldn't we need to know the final
velocity in order to know that the acceleration is constant?
When we measure average velocity at a certain time, is that time farm specified. For example are we
measure in the velocity at a certain time like 15 seconds - 18 second? Is it measured in a specific time
frame like 1 second, 3 seconds...ect?
When we are calculating instantaneous acceleration do we have to account for both x and y acceleration?
With the equations that we learn in our class, can all of them have constants that "wander around"?
Why can the acceleration be defined as deltaV/deltaT if acceleration is constant (logical explanation)? Is
there another variable if acceleration is not constant?
if the average velocity is the same, does that mean that the acceleration is constant?
When graphically calculating the average velocity, the area under the imaginary line drawn between the
endpoints (pink and blue regions) should equal the shaded area under the true velocity?
What is the significance of the removal of the subscript in the calculation of the final velocity from a
constant acceleration? Isn't t2 hypothetically treated as a variable already?
How often will we see constant acceleration in our class? Is constant acceleration more common or less
common?
Why is it that we changed t2 to constant t when it was the final time? Can we just ignore the final time in
the equation and still solve for v2?
How do we calculate velocity if the acceleration is not constant? Can we?
Can t1 become a variable instead of t2? Does it matter which constant becomes a variable?
Are there relevant biological systems that operate on a constant accelerate, or is this more often used as
a "toy model?"
Can you give us an example where we would have to consider the angle of the motion and use i-hat and
j-hat?
I'm still not quite sure why physic often let a constant "wander around" to become a variable. Therefore, I
don't understand why "t2" can be replaced by the variable t in the equation v(t) = v1 + a0 (t - t1). Can you
please explain this?
What would happen if the constant acceleration increased then decreased at a uniform rate? Would it be
zero?
Since we can calculate average velocity from constant acceleration, is there a way to calculate
instantaneous velocity?
What does the area under the curve mean, the blue area?
If the velocity is constant in an object's motion, then does this mean its acceleration is also constant? If
so, how is this possible?
Why is it that in physics, a constant is allowed to wander around while a variable can be fixed at specific
value?
How do we account for the fact when delta x is a person returning to where they began? Average velocity
would be 0?
"If we want to figure out what the average velocity in that time interval is, we have to find the constant line
so that the areas under the true velocity curve equals the area under the average velocity line (a
constant)." How do you determine this? The next sentence says to make sure the pink and blue areas are
equal, but how do you make sure they are equal? What if the slope is different? What if the acceleration
isn't constant?
Is it safe to assume that constant acceleration can be found for any linear function?
What is the purpose of removing the pink area from the graph and adding the light blue area? is the area
they represent not already present when the area under the curve is analyzed? Or can the midpoint be
arbitrarily chosen and those those two triangular areas are required for adjusting the midway point and
the average-given that the graph is representing a constant equation?
If the velocity is equal to the midpoint of the graph, does that always mean the acceleration was
constant? Is there ever a case when this isn't true?
For the final velocity equation
v2 = v1 + a0 (t2 - t1)
These constants can be chosen to move. In particular, let's call t2, "t", and treat it like a variable. Then we
can see what the velocity looks like as a function of time.
Depending on the questions were given on the test, we can move the variables around this equation to
find out a specific velocity, acceleration or time?
Another question for a part of the article:
"These three equations (or 4 if you count knowing what a delta of something means) each have a clear
and straightforward conceptual meaning and let you calculate whatever you need from whatever you
know when the acceleration is constant."
The three equations given in the article all can calculate what I need from whatever I know when the
acceleration is constant, but in which situations may one be more favorable?
How can we differ the acceleration of the velocity compared with the acceleration of something's speed?
When we are given a graph where we must calculate the average velocity, how do we determine the
amount of adjustment we have to make on the average velocity line, to find the constant line?
If accelration is a constant, why does it change?
If acceleration was not constant, would you need to have a delta sign in front of it?
If the light pink area and light blue are are used to find the average velocity, what does the darker blue
area under the graph represent?
So is it correct to say that average velocity is always a constant and acceleration is always a constant as
well?
Is there a way to solve for average velocity if there is no constant acceleration and in return no constant
velocity?
Is there a way to find the average velocity when acceleration is not constant? Would you just that the
average over the period of time when it is constant on a smaller scale?
In the real world, everything is not always moving in constant acceleration. Why don't we solve more
problems incorporating acceleration that is not constant?
How would these equations work if acceleration was not constant? Could you still make something a
variable and plug in?
What if acceleration changed but the average acceleration was constant, would the average velocity still
equal (v1+v2)/2?
How can average velocity be (v2-v1)/2 and be (v2-v1)/(t2-t1)?
This means that if we have a constant acceleration, we can also expand the velocity equation and figure
out the positions of the object, as well?
When replacing t2 with "t" and treating it like a variable, what would we do with the actual t2 number?
Can we use constant acceleration to solve for aspects of position?
I am still not quite understanding the difference with velocity and acceleration, i know the difference but
the math part is confusing me. If acceleration is constant shouldnt the velocity stay the same or is that not
the case?
Does the area under that v(average) line equal the displacement between t1 and t2?
so is the article stating that to be able to find the average velocity using the two endpoints the
acceleration must be constant?
Can you calculate the change in time when acceleration and velocity are given, how does that work out
dimensionality wise?
Will we always be assuming constant acceleration? Also referring to the three equations at the bottom,
can we plug one equation into another?
For the figure with the graphs, why is " the average velocity...halfway between the endpoints"?
How would you calculate the average velocity if acceleration wasn't constant?
So if you don't have a constant acceleration is there no easy, straightforward way to calculate the velocity
or speed at certain times?
is acceleration just the 2nd derivative of position vs time graph?
How is the equation "?x = <v>?t" derived? I am not sure how average velocity multiplied by time gives
position.
Doesn´t it give misinformation when you fix a variable at 1 value and the other way around?
Will the constant accelerations be affected when it is negative? Negative velocities do not mean the same
thing as negative accelerations so how can they be used to calculate velocities at other times?
From the four equations :
"[delta]v = a [delta]t or v2 - v1 = a [delta]t
<v>=(v1 + v2)/2
[delta]x = <v>[delta]t"
is it possible to move terms around to get an equation to relate acceleration with position?
I saw in the Acceleration page http://umdberg.pbworks.com/w/page/68375732/Acceleration%20(2013) an
equation like "a(37) = [v(37.5) - v(36.5)]/[delta]t = = [x(38) - 2x(37) + x(36)]/[delta]t" which did relate
acceleration to position, but is there one that can be used in any circumstance?
I don't understand why we needed to change t2 in the equation to t, don't the equations still make sense if
we had not?
How small do we actually define the time interval when doing these equations. An interval of 10 seconds
will have a different acceleration than an interval of 1 second, so how small do we usually define the time
interval?
Can you combine two different motions each with different constant velocities to get a grand total of
average velocity?
Is it realistic to think of acceleration as a constant when most objects are probably not accelerating at a
constant rate all of the time?
Would the value of acceleration be negative if you had an object that was traveling at a decreasing
velocity instead of an increasing one?
How do we know when we should let a constant "wander around" or fix a variable at a specific value?
If a graph of a system accelerates at a constant rate and then decelerates at the same constant rate for
the same amount of time, what will the average acceleration be? Will it be zero?
If it has been defined that velocity must have a direction to be considered a true velocity, would the same
apply for acceleration even though its the derivative of velocity?
More often than not, the acceleration will not be constant. How do these equations have to change to
make up for that?
If the velocity is constant, doesn't that mean that the acceleration is zero? (i.e a flat horizontal line when
graphed)?
Are we able to assume, or is it possible, that anything can have a rate of change, such as velocity is the
rate of change of position, acceleration is the rate of change for velocity, and so on?
Can you write acceleration as a vector?
Why for constant acceleration do you divide the average velocity equation, <v> = (v1 + v2)/2, by 2?
what does the subscript 0 mean when placed next to acceleration?
Later in the course will we keep the i-hat and the j-hat and consider the changes of the angle of our
motion?
Why does the area below the average velocity line have to equal the area under the true velocity curve?
What does it really mean?
Is it really okay for us to just "drop" the i-hat and j-hat when we assume that we are moving down a line?
What kind of information might we be missing if we do that?