Calculating with average velocity
I'm a bit confused on the constant acceleration example.
Assuming that we found a certain average velocity for our journey between two points ignoring any times
that we went back and forth, and then calculated the time, based on the distance between the two points
and the average velocity. It seems like this time would then not account for the time that was lost going
back and forth between the two points. It would only talk about an ideal condition in which we started from
one point and without stopping, or going back and forth, reached the other point. Wouldn't this then be
non-realistic?
Is it accurate to say that acceleration is equal to change in velocity/change in time?
I'm still confused, what's the difference between calculating the average speed and the average velocity?
Are there any situations where <v> = Δx/Δt or <v> = (vi + vf)/2 won't work for calculating velocity?
So with average velocity is that the pace you need to do in order to have the same displacement you
started with even though you may have stopped and started ("a mess")?
If acceleration is a derivative of velocity then can you take the second derivative of a position function to
find out the acceleration and totally bypass considering velocity?
when we have a constant acceleration, does it mean we also have a constant velocity, or our velocity is
changing in a constant rate?
How do we calculate the average velocity from acceleration if the acceleration is not constant?
To find the average acceleration, wouldn't you need to find the average velocity so wouldn't the "Special
Case" section not be a very applicable problem?.... Since you need the acceleration to assume the
equation given.
If we are going at a uniform rate, say a constant acceleration x, would that be the same thing as saying
we are going at a constant velocity x? I know they have different symbols, and we cannot use them
interchangeably.
When would constant acceleration apply to a biological system?
How does the constant acceleration affect velocity?
Didn't we just say that delta x isn't distance traveled, it's displacement? How do we know when to
consider direction and when to look at just numbers?
If there was no change in the velocity over time, wouldn't the average velocity just be zero?
Did this article explain how acceleration is the derivative of velocity?
If each equation is just rearranging the original equation without adding anything, how does each
equation tell us something different? Can you just use the original equation and solve for the unknown
variable?
In what case would we see a uniform rate? And in that case, would it truly be necessary to determine the
'average velocity' since It is held constant?
Can an average velocity be negative if you set one direction as positive and you are traveling in the
opposite direction"?
I don't quite understand how <a>=a0 represents a constant acceleration?
Why does the average acceleration = (Vf+Vi)/2 if given constant acceleration? If you start at velocity zero
and end at a certain velocity would dividing that velocity in half give you the average?
How do you calculate instantaneous acceleration from average velocity?
Why is constant acceleration a "special case?"
Are these values dependent on direction? What is the absolute value of acceleration called?
What if you are given average speed, could you then find average velocity?
Why is the constant acceleration indicated as <a>? I thought that symbol meant average.
Is calculating with speed different from calculating with average velocity?
Does taking the first and second derivative always give you velocity and acceleration respectively? Or
can they mean something else?
Will we have to use those two equations for rate of change to prove the kinematics equations provided in
the link on that page?
Is constant acceleration relevant to any principles regarding biological organisms?
Can we only use the constant acceleration equation when velocity is changing at a uniform rate?
If your time interval is really small are average and instantaneous velocity the same?
If velocity is the derivative of position, and acceleration is the derivative of velocity, what is the derivative
of acceleration and is it important knowing it in the context of this class?
Can average velocity not have directionality? Could average velocity be calculated of a car going south,
then north, then east, and finally south again?
Why does the variable for distance keep changing?? For example, in this reading, distance is shown as x.
Wouldn't it be less confusing to leave distance as D?
Average velocity is calculated using the distance traveled over the time taken. So, say I'm on campus
walking a mile, but I stop every .25 miles to talk to a friend for 5 minutes. When calculating velocity would
those 5 minute stopping intervals be counted in the time taken? Or is the time taken just counted during
the times when I'm actually walking?
If velocity is changing at a constant rate (ie. constant acceleration) wouldn't that mean the acceleration is
0?
Why are the "stopping, starting, back and forth" motion not heavily considered in the average velocity?
Isn't it an important aspect of our calculation of velocity?
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Can the formula <V> = (Vi + Vf) / 2 be used even if the acceleration isn't constant? Or can it be used for
any average velocity problem?
Why do we take an average of initial and final velocities in order to get average velocity when velocity is
changing at uniform rate
Is acceleration a vector or a scalar?
Acceleration can be described as an increase in speed, decrease in speed, or change in direction. How
can we differentiate between these three types of acceleration, based on the value?
How can we use average velocity calculations in biology?
In life outside of class, when will we be given the average velocity and than have to figure out the object's
initial or final position or the start or stop time? How can a velocity of an object be known without knowing
its change in position and change in time?
Since acceleration is the derivative of average velocity, is there ever a point where an object has 0
acceleration even when it moves, similarly to average velocity?
Can acceleration be greater than zero if velocity is zero? I am thinking of a scenario where an object's
total displacement is zero, hence having zero velocity, but is displaying high acceleration from point A to
point B to point A.
If acceleration is constant and positive (a horizontal line on a graph), then velocity increases in a linear
manner, does displacement increase exponentially? What does displacement look like on a graph if
acceleration is increasing constantly?
What is the best strategy to go about calculating the average velocity of 2 competing thing that have
different units of motion?
Can acceleration be negative?
Averaging the velocities of individual objects is not the same as the average velocity of all of the objects
combined, correct?
How does calculating with average velocity change, as the dimensions change?
It says in the reading "If the velocity is changing at a uniform rate (constant acceleration so <a> = a0,
some constant), then it's pretty obvious that over a time interval in which the velocity changes from vi to
vf, the average velocity will be the average of the initial and final values," would an instance like this, in
which there is constant acceleration, cause any change in the calculation of instantaneous velocity?
Can you show an example of how we can use all three of the equations in the constant acceleration
section in one problem? I have only ever used them individually.
When would average velocity be helpful in a problem? It seems like it disregards a lot of motion,
especially if you are just using the initial and final velocity, so I don't see how this would be an accurate
measurement of velocity.
According to this equation: average velocity = (distance traveled) / (time taken)
If velocity is described as a vector, then why don't we include the direction in the equation? why does it
just mention "distance traveled"?
What will happen if the acceleration is not constant. Can we still use the same equation?
What is the relationship between constant acceleration and velocity?
Does acceleration also have derivatives? How does acceleration change compared to velocity?
Do we have a standard unit of measurement for the equation? For example, is velocity going to normally
be meters per second, time in seconds, and distance in meters?
How come we don't measure average velocity by distance traveled in general. if we end up at the same
point we technically didn't go anywhere, but we still traveled and came back to the same spot so why
don't we measure it by the amount of feet/miles we went as opposed to a starting and stopping point?
I am having trouble understanding how at constant acceleration, the average velocity is only calculated by
the average of initial and final samples. Why is the change in time not factored here?
Instantaneous velocity can go both ways, or in two directions. does that mean that the average velocity is
the calculation of the instantaneous velocity?
Can you calculate average velocity from only time and acceleration?
A velocity changing at a uniform rate denotes a constant acceleration, so does that mean that the
average velocity can only be the average of each time inerval when <a>=a0(subscript)?
From the average velocity example, if all four runners had run for the same amount of time would simply
adding the average velocities of each runner provide the overall average velocity of the team?
So are average velocity and acceleration equal since they both measure a change in position/a change in
time? I'm having trouble understanding the difference between the two.
Will we need to use this form of equations specifically on any problem? Or can we always just remember
delta means change?
So if we have a word problem and we have those equations, aren't we technically solving for "x"? The
difference in these problems is that "x" has a unit, right?
Can an object have increasing speed while its acceleration is decreasing?
How do the different dimensions of velocity and acceleration affect the process of deriving velocity?
Since average velocity is based on the displacement, if displacement is 0, the average velocity is 0. In
what real life situations would finding the average velocity be useful over calculating average speed when
the displacement is known to be 0?
In the text, it is said that if the velocity is changing at a uniform rate, then we may find the average velocity
by the equation <v> = (vi + vf)/2. However, how would we find the instantaneous velocity at certain time
period?
Is the average velocity used to describe the "big picture" and the instantaneous to examine it in detail?
Can't the equation used to determine constant acceleration also be used to determine acceleration at any
point with a velocity graph. Wouldn't vf just be the last point being compared to and the vi being the initial
point chosen instead of vf & vi being the final and initial of the whole series? So what makes this constant
acceleration equation unique?
what value does the derivative of acceleration give?
And does it follow the same laws like dx=vdt and dv=adt?
Further building off my last 2 questions, I was able to infer or interpret that acceleration is a manipulation
of the velocity equation. I also remember from previous classes that acceleration can be defined as the
second derivative of an equation in a position graph. Is this true?
How would the equation change is acceleration is not constant? Or would it be a different equation
overall?
I do not understand the special case example with constant acceleration, specifically the last equation
listed in that section. When would this be used over the other equations?
To clarify, velocity isn't just the speed at which you traveled but the distance traveled? So person A and B
could have traveled at the same speed but if the path for person A was shorter and took less time than
person B, person A would have the faster velocity?
Are we required to find the average velocity before finding the constant acceleration or is there a direct
way to go from displacement to constant acceleration?
How do you know which of the velocity equations to use if it is not directly stated in the problem?
<a> = a0 = Δv/Δt = (vf - vi)/Δt. How can the velocity be changing while the acceleration stays the same?
what's the difference?
In a case where velocity is not constant, is there a method to indicate that there the velocity isn't constant.
Would one just have to take the instantaneous rate at various points to demonstrate that the velocity is
slower at one points and faster at others?
If we were to use velocity in a calculation to find how far we traveled, wouldn't the answer be kind of
useless? Like if I wanted to know how far I traveled during a round trip to California, the answer would be
0 miles. Or am I misunderstanding this?
The deltas seem seem puzzling to me. If it's the "distance traveled" and "time taken" why is it change in
distance traveled divided by the change in time? Is the delta for comparing different velocities in different
positions?
If velocity is a measure of displacement, would acceleration be described as a rate of displacement?
How do you calculate the average velocity of something with an exponential rate of change?
If there is a constant acceleration, then it is safe to simply add the initial and final velocities and divide by
two?! How is that equivalent to calculating delta v by delta t?
is acceleration the derivative of velocity?
Constant acceleration, I still don't understand how to calculate that?
I'm a little confused, can we account for the starting, stopping, back and forth by using the three equations
on the page?
How does knowing that delta means change help you to avoid memorizing other equations
What is the difference between average, instantaneous, and constant velocity?
The equation for average velocity can also apply to several special cases. For these special cases, are
things being added to the original equation or is it simply a derivation of the original average velocity
equation?
The reading tells us that average velocity is displacement over time while the equation in the textbook for
average velocity is (x2 - x1) / (t2 - t1). If we used the textbook equation, wouldn't it mean that if a mouse
started at a rock, ran 0.5 meters to a tree and then ran back to the rock, the average velocity of the
mouse would be 0 because the mouse started and ended in the same place? Using displacement over
time like the online reading said makes more sense to me.
What would be an example of something that satisfies the special case listed where acceleration is
constant? This would help me make more sense of the scenario.
Does it make any conceptual sense to deal with higher order derivatives of velocity beyond acceleration?
Why can't you just average the averages when calculating average velocity in the 4x100 relay example?
In the real world, we are not always moving at a constant velocity for an entire designated time period.
There are times where you may be moving at a different velocity than you were before. How are we able
to calculate these different velocities?
The paper stated that the average velocity will be the average of the initial and final values. Does this
concept work for acceleration as well?
What if an object traveled in three different dimensions, would there have to be three different velocity
equations to account for each direction/dimension?
So constant velocity and constant acceleration are the same thing? How do we keep track of these
equations?
Most of the time calculating with average velocity can be very convenient. I agree with that. But in the
cases that we are also interested on how we got there, for example; if the object stops or goes back and
those sort of behaviors, what are the best ways to calculate including those changes?
Could average velocity and acceleration ever be equal to each other?
is there an equation for acceleration or is it the derivative of velocity?, also if we get a fixed number for
velocity that will make the acceleration 0 ( taking a derivative of a constant = 0) ?
If we were to represent an object in constant acceleration using a position vs. time graph, would the graph
be a straight line? Would the velocity be the slope of that line? And since the velocity will remain constant,
does that mean the velocity vs. time graph would be a horizontal line?
is there a way that we can still calculate for both missing variables -displacement and time- just given the
average velocity?
When calculating distance traveled does that include the backward direction also, if so would you subtract
it or add it from the total average velocity?
Is there some notation that distinguishes average velocity from regular velocity?
Is the value of acceleration always less than or more than the value of velocity? Or is it completely
circumstantial?
Because your velocity is zero no matter how far you go from your original point as long as you come
back, would there be any situation regarding sports where velocity would be needed to figure out
something pertinent?
If we walk backwards then forwards again, do we count the forward distance that is travelled twice?
Is there any measurement to account for a changing acceleration over time, or is that foolish because
acceleration is a change itself? In other words, is acceleration the last derivative that we need to worry
about?
shouldn't velocity be measured in total distance traveled/time not just distance displaced?
In previous physics classes, we did not use the notation, "<v>" for average velocity, so is this a mandatory
notation we have to use on homework and exams?
Why does <a> = a0 = ?v/?t = (vf - vi)/?t not count for irregular acceleration?
How do you know when the acceleration is constant from the average velocity?
I took AP Physics in high school, so I remember a little from the Kinematic Equations. I could see how
they got vf = vi + a * t, but how do they get dx = (vi + vf)/2 * t, because to get vi and vf you need dv, and
the only equation I know for dv is in relation to acceleration; yet this equation only has dx in it without
acceleration. How is that possible (unless there is some equation that I just don't know about)?
Is it possible to have a graph with constant velocity and acceleration, or does constant velocity assume
no acceleration?
What about cases when the acceleration is not constant? In that case, how do you figure out the average
velocity?
Could we calculate the average velocity if a path included constant acceleration and constant
deceleration?
So average velocity only matters on the starting point, the ending point and how long it took to get there?
What kinds of questions and problems will require the three equations mentioned to be used? Will we see
an example of this?
If one objects velocity depended on the velocity of another object, for example a Lamborghini dragging a
boulder, would the equation we would have to use to calculate the velocity of the dragged object change?
How are the derivative and the average velocity related?
Are there any biological examples of constant velocity and constant acceleration? Or is this more of a
hypothetical, special case situation?
The constant acceleration special case says that in this situation the average velocity will be the average
of the initial and final values. I'm just confused about how this is any different than when you take the
slope of the initial and final values to get the average.
When would a biologist need to calculate and use avg. velocity in the field?
Would taking the individual instantaneous velocities and making an average of those be a more accurate
measurement of average velocity than taking the overall highest and lowest velocities or would it be the
same value?
When is a good point to begin using derivatives rather than using the averages? When is the delta small
enough to be negligible?
To calculate average velocity, why can't we add a set of velocities and divide them by the number of
sets?
Wouldn't it be impracticable to use average velocity in the real world, since nothing actually ever moves in
a straight line in nature, and so average speed, or distance over time, would be the general accepted
notation for moving objects?
is it possible to have a high acceleration but with an average velocity of 0?
I've never seen the brackets before when referring to velocity. Is this used on math courses?
How can <a> be equal to, <v> = (vi + vf)/2, when the acceleration is found by taking the derivative of
velocity?
Is there a time when the velocity is some constant and the acceleration is 0?
On tests will we be calculating constant velocity and acceleration or will we go on to learn other
scenarios?
Since velocity is a vector quantity is acceleration also a vector quantity?
In the special case of constant acceleration, what sort of things can we determine from those equations?
What do those things tell us? Why is constant acceleration such a special case?