Reading the content in the kinematic equations
Can we have an example in which we solve for instantaneous velocity and acceleration. I understand that
i need to take the derivative of the change in position over the derivative of the change in time to get an
instantaneous velocity but what does the calculation actually looks like, the word explanations aren't really
giving me a mental picture of how I would approach a problem in which i would need to use this.
On our physics tests, If one does the calculation or interpretation correctly but forgets to right the equation
that suits motion in a particular direction, instead only writes the general equation, will the student be
penalised and by how many points?
Why do we change "x" to "r" when vector comes into place?
Why are we focusing so much on symbols?
Is there a way to take an instantaneous velocity or acceleration without using a derivative? Do you just t
to a very small number and calculate?
In a real world it takes lots of energy to stop a heavy truck than it takes a car to stop. In non of the
equations from the reading, there are no difference. Where does mass, gravity and friction get involve ?
Why do we use (f') to denote a derivative in math classes, but we use Leibniz's notation in this class? Is
Leibniz's notation more accurate when using derivatives in physics, or was it arbitrarily chosen?
Will we need to use the notation t1 --> t2 in average velocity and acceleration or will it just be something
that can be used to more explicitly denote that we are doing something to a quantity.
If dx/dt has units of distance/time just like (delta x)/(delta t) , aren't equations A and B the same, as are
equations C and D?
Are the equations listed the only ones we will be using? Will we be expected to build more complex
relationships off of the equations?
I dont understand the averages part with the brackets?
Are there cases when the motion of an object in one dimension is dependent on the motion of that object
in another dimension?
What do the equations look like when we're calculating instantaneous acceleration? Would they look the
same?
Can we go beyond what is shown in this article and determine how acceleration is changing? Aka derive
acceleration?
Is it always necessary to put subscripts with the velocity and acceleration equations (i.e. t1 -> t2) or can
that be left out?
I had a difficult time understanding the portion of the reading explaining vector equations in terms of the
triples (x, vx, ax), (y, vy, ay) and (z, vz, az). Would you be able to review this during our Monday lecture?
With all these terms, and symbols in physic equations and formulas. How are we suppose to keep track
of the complexity? Is there an easy way to think of the different parts of an equation?
So we only need to use the brackets <> around a and v when we are finding the change (?) in
velocity/acceleration?
Is there a notation that is used to indicate instantaneous acceleration or velocity?
How does Leibniz's findings differ in a way that it is favored by the physics community?
I had trouble understanding this: "This means that instead of four equations for the set of variables (x, v,
a), we have for equation A, B, C, and D for each of the triples: (x, vx, ax), (y, vy, ay) and (z, vz, az). There
is a set for the motion in each dimension and they are independent of each other."
Is instantaneous acceleration or velocity simply the average acceleration or velocity during a time interval
that is approaching zero at a designated point? Are the two terms not equivalent in anyway?
Does it really matter if you use dx/dt instead of d/dt? What is the real difference?
In the first set of equations shown, it says that " (A and B) tell us how the position changes (velocity); the
second row (C and D) tells us how the velocity changes". Isn't that the same thing? To me, it's saying that
both sets of letters are measuring the velocity, so I was confused.
Can a velocity be negative? If so, what does the negative mean?
Why are we not using the kinematics equations?
What is the point to having two different types of the velocity and acceleration equations? I'm assuming
the notation is different because one form (delta form) should be used for average while the derivative
form should be used for instantaneous? Wouldn't we get the same values regardless of which form we
use though?
Is there any situation where the kinematics equations in the physics textbook are a better alternative than
these derivative equations?
What could be an example of a motion in multiple dimensions where vector equations must be used?
how do you take the derivative of a constant?
If v and a are meant to represent velocity and acceleration in kinematic equations, respectively, what
does r represent when considering vectors?
I am still a little confused on the difference between velocity and acceleration.
Besides the dot in Newton's equation and "dx/dt" in Leibnez's equation, is there a significant difference in
using one or the other? a
What exactly does it mean if something is a vector? Does it mean they have a direction?
How do the calculations for a vector correspond when the vectors are added and multiplied?
If v and a are functions of time, why do we not write it as v(t) and a(t) to avoid confusion?
I am having a difficult time visualizing these kinematic graphs. What do you suggest is the best way to go
about this visualization process? Is there a trick? Is it easier to visualize the velocity first and work
backwards to the position, or always begin with the position?
Will we need to go passed acceleration, and start using its derivative? What is the derivative of
acceleration?
I am unsure of what exactly Leibniz's form means. Could you explain it more in depth or apply it to other
physics concepts?
How do we describe which direction the subject of interesting is moving to using vector sign
If a vector describes motion in a straight line, then if an object is not moving in a straight line, how do we
describe its motion?
How do these things relate to forces?
Is there a way of combining all three dimensions in a 3D system into one equation? Is this usually done,
or are they usually separated into three equations for clarity?
In math, delta and d are used interchangeably when looking at rate of change. With respect to velocity
and acceleration is delta only used to describe average rate of change and d only used to describe
instantaneous rate of change?
Can the brackets and the delta be used interchangeably? Although the brackets represent the average
whereas delta represents change, don't these have a similar meaning?
Did most mathematical notations originate entirely arbitrarily? Are they standardized or does everyone go
by convention/preference?
If a vector describes motion in a straight line, then if an object is not moving in a straight line, how do we
describe its motion?
When considering motion in multiple directions, do we add vectors together in order to reach a net value?
is it always appropriate to denote delta x if changes still occur from x3-x2+x1 of should you use two
separate equations?
In the reading it says that there can be "a set for the motion in each dimension [of the triples] and they are
independent of each other," is there any instance in which the dimensions would not be independent of
each other? If so what is an example of this?
Why do you need to have equations A,B,C, and D for x,y and z? Are you just trying to say that you can
use the same equations for the variable (x,y,z) but that they are not in an equation together?
What is the difference between the equations with the delta sign and the equations written with "dx"?
Do we only use derivatives when calculating change at an instant (non-zero interval)? And is that why we
do not include the brackets when we need to take the derivative?
Will we be using the prime notation if we are looking for derivatives
Are the delta's and derivatives the same thing?
To calculate velocity and acceleration for vectors, do we add the values of equation A, B, C, and D of
each direction x, y, and z? Or do we leave the values for x, y, and z as separate numbers?
I don't understand how B and D specify specifically instantaneous change. Wouldn't you be able to write
instantaneous change for A and C, by taking away the brackets? How does "the change in time" imply the
total average change while the "rate of change" from the derivative implies instantaneous?
i am confused by velocity at a certain time. At time it says it is "essentially zero interval" and others it says
it is at a "small time interval." What exactly is the time we use to measure, is it given or assumed?
For motion more than just a straight line, what does the (z,xz,yz) represent?
I am having a hard time grasping that v and a represent functions of v and a and are not actual values. I
am confused because when we are solving those equations, aren't we getting values as answers?
I am sure we will be using these equations a great deal in the future for problem solving. However, could
you explain how these equations only hold for motion in a "single dimension" or along a straight line?
Does this mean it only applies to objects that are moving forward, but not backwards or sideways?
so is using the kinematic equations the same thing as solving for derivatives?
What is the overall difference between ^(Greek delta) and d? Don't they both represent
change/derivative?
If these equations always hold, why provide another equation for constant acceleration?
Instantaneous velocity and acceleration tell us how something can change in an instant while average
velocity and acceleration tell us how something changes over a time interval. Considering how
instantaneous and average velocity and acceleration depend on the same data of time, wouldn't their
graphs look similar or have some sort of relationship with each other?
Should we memorize all of these equations?
Why don't they write a and v as a(t) and v(t) to avoid confusion?
Why is the delta symbol in the average equations (such as change in position or velocity) chained to be
derivatives in the instantaneous equations? Is this an arbitrary change, or is there a larger principle
behind it?
In a given problem, what kind of scenario would hint at the idea that we would need to consider motion in
the z dimension, in addition to the x and y dimensions?
How would having vectors (motion in dimension) in equations differentiate equations without the vectors?
Why is considering vecotrs important in physic?
How are equations A and C different from B and D? I understand that in A and C we are looking at the
change in time, whereas in B and D its the rate of change, so if the rate of change is time are they not
describing the same dimension?
When using vectors, what indicates the exact direction in which an object may be moving?
If you are not given the velocity, can you make an equation relating avg and inst. acceleration with
displacement?
I am confused as to why these equations are referred to as kinematic equations. is it because these
equations describe the motion of an object and it's speed?
Will we ever have to use Newton's form in this class? If so, for what kinds of scenarios?
Is it incorrect to write an equation with the <> but without the delta? Is equation A another way to write
equation B and vice versa?
It says that we use v and a instead of v(t) and a(t). Why don't we use these standards if in fact the
equations for velocity and acceleration are dependent on time? Isn't the 'math' notation more correct?
When is it okay to omit arrows on an equation? Can you give an example of where arrows can be omitted
and where equations require the use of arrows?
In terms of vectors, If we wanted to signify that we were analyzing the <v> and <a> in two directions,
positive and negative, would we indicate that with two arrows in their respectively positive and negative
directions? --> and <--- ?
Can we find the instantaneous rate of change in velocity as an object changes direction, or are we limited
to time intervals?
"< > -- The brackets around the v and a in equations A and C indicate that we are considering the
average of the quantity contained inside them. An average implies an average over some interval.
Therefore, the equations containing this symbol implicitly refers to a time interval, not just a single time."
So in the above excerpt from the book, is the answer going to be a specific interval rather than just an
answers. I'm confused what would come out of those equations. I know the arrow represents a vector, but
how do these equations (a,b,c,d) differ from the other 4 equations listed before?
How would we create a kinematic equation for something that does not have a constant acceleration?
When we are calculating rates of change with respect to vectors, are you saying that equations A through
D hold separately for each coordinate plane, x,y, and z? What if the motion of an object hits though more
than one plane, how do we solve for the overall velocity, and acceleration if these equations are
independent of each other?
What does it mean to be a function of time?
Why is r used instead of x in the vector equation for velocity?
Can these equations ever be used in conjunction with one another?
Can you explain why the kinematics equations in typical physics textbooks only hold for the case of
constant acceleration?
What is the difference between the kinematic equations vs. the vector equations that we need to know for
this class?
Since the derivative of a function is also a function, does that mean that you can take the derivative of
acceleration and then take derivative of that too? Is there ever a point where you can no longer take the
derivative of something? What is the derivative of acceleration and the derivative of that and does it have
a physical equivalent like velocity and acceleration? If it does, is there ever a point it would reach that it
wouldn't?
How will we know which kinematic equation is appropriate to use when interpreting a problem?
For each of the triples: (x, vx, ax), (y, vy, ay) and (z, vz, az), are these for three separate equations? Or
are the 3 parts of the triples for four equations listed in 5 (A, B, C, D)?
*
How do you relate the dimensions of position, velocity, and acceleration?
When do we use r versus x to describe position?
Equations A & B plus C & D look both groups really similar to each other for my eyes. Even though I know
one represents average and the other one is meant for a specific instant, what would you recommend for
me to take in account at the moment when I have to pick one and apply it in a physics problem?
If we labeled a derivative something other than dx/dt, for example using x prime, would we be marked
wrong on an exam/homework for that?
Do we need to memorize the kinematic equations?
can you explain what the difference in the mathematical equation with the Delta and the d
?
Why do we use a different notation for derivatives if it means rate of change (delta x/ delta t)?
So will the delta implicitly always refer to the same interval as to what the brackets are already telling us
to refer to?
Why does an equation need to have a vector value on both sides of the equal sign?
Is calculating the derivative for a vector any different from calculating the derivative of a non-vector?
Is it possible to have a negative rate of change for velocity but positive rate of change for acceleration and
vice versa?
When you use the "d" notation, the webpage says its a derivation, so are we given the velocity if we need
to get the acceleration, since acceleration is a derivative of velocity? Also, how do we get a specific vector
of velocities in two different positions?
To eliminate confusion, why not just combine the delta, d/dt, <>, t2-t1, and other relevant symbols and
notation into one system? Also, will multiple different symbols be used on one exam/ assignment?
how can you measure the velocity of an object changing directions in 3D system?
In the reading it says that these equations are used for linear motion but how are the equations
manipulated for circular motion?
Are the brackets also used when considering a very small difference (close to zero) to make the average?
Do we need to calculate derivatives from graphs mathematically or just know the general pattern of the
graph?
One of the kinematic equations I learned in high school was "v^2 = v0^2 + 2a(x-x0) [treat 0's as
subscripts]". How did they get an equation without time in it?
Since we use the notation d/dt, does this mean that derivatives are ALWAYS with respect to time? Is it
possible to see how acceleration changes as our distance changes?
Does it matter whether we use certain symbols or not? For instance can I use v(t) instead of v when doing
an assignment?
In the first figure. where equations A, B, C, and D are all being compared, wouldnt A and B be giving the
same information as C and D? I ask this because all 4 are giving information on how the velocity
changes.
Do we ever look at these variables (position, velocity, acceleration) as anything other than functions of
time? Why is time always so important in physics?
Are there any other vectors for acceleration/velocity or is the arrow universal for meaning that an object is
in motion?
How is it possible that the equation sets for motion in each dimensions are independent of each other?
I am struggling to fully grasp the concept of how an object is moving. What is the difference between
"how" and object is move and "when and where" it is moving? Wouldn't "how" just be a sum of when and
where it is moving?
Since velocity and acceleration are both functions of time, why would it not be suggested to write them as
v(t) and a(t) rather than v and a?
When there are multiple vectors in a problem, can we add more than one of the equations together to get
a final value for the movement of the object?
In order to calculate instantaneous velocity or acceleration, do we still have to consider some type of time
interval, even if it is really small?
If the delta triangle implies that the equation is already over a time period, then wouldn't the delta x/ delta t
be redundant since you are already implying that it is over a specified time period?
Is velocity just acceleration with direction? Why wouldn't we just always use velocity if it's more precise?
Since there is an equation for both velocity and acceleration, is there one for position?
Are x and r interchangeable in these equations or do they represent different things?
When calculation instantaneous velocity or acceleration is it acceptable to put the time being studied in
parenthesis? For example v(1)= or a(1)=
So for vectors, we can only work with each set of variables one at a time? When would we need to work
with more than one set?
Why don't we write the symbols for velocity and acceleration as functions of time as v(t) and a(t) like we
would in a standard math class? Is it for simplicity or is there a more philosophical reasoning behind it?