Kinematics and Graphs

[MedPR]

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Ok, that thread about v/t graph got me all confused.

I don't need the explanations (I will hopefully be able to explain it to myself), I just need the facts.

For a displacement vs time graph.
Slope = ?
Area under the curve = ?

For a velocity vs time graph.
Slope = ?
Area under the curve = ?

For an acceleration vs time graph
Slope = ?
Area under the curve = ?

 

[MT Headed]

Ok, that thread about v/t graph got me all confused.

I don't need the explanations (I will hopefully be able to explain it to myself), I just need the facts.

For a displacement vs time graph.
Slope = Velocity
Area under the curve = Absence*

For a velocity vs time graph.
Slope = Acceleration
Area under the curve = Displacement

For an acceleration vs time graph
Slope = Jerk*
Area under the curve = Velocity

I am on my phone, it was easier to answer them inline in your quote.

I put a * next to those that are not relevant for the mcat.

The slope of Jerk* is Snap*, for what it is worth.

The unit of Absence* is the meter-second and is a measurement of absence (or loneliness), the idea that being 5 miles from home for 10 days is just as absent as being 50 miles from home for 1 day, for example.

 

[MedPR]

I am on my phone, it was easier to answer them inline in your quote.

I put a * next to those that are not relevant for the mcat.

The slope of Jerk* is Snap*, for what it is worth.

The unit of Absence* is the meter-second and is a measurement of absence (or loneliness), the idea that being 5 miles from home for 10 days is just as absent as being 50 miles from home for 1 day, for example.

Thank you much.

 

[milski]

On the phone too but disagree with some points. What he has are the integrals, not the areas. Class starts, more later.

 

[MT Headed]

True, when you say area under the curve, I read it as literally under... as in if the curve drops below the origin then the area under the curve has to be negative because it is now 'above' the curve.

EK sometimes plays games by asking for the area 'between the curve and the x axis' which is a different concept and would measure distance, not displacement, on a velocity vs time graph.

 

[MedPR]

True, when you say area under the curve, I read it as literally under... as in if the curve drops below the origin then the area under the curve has to be negative because it is now 'above' the curve.

EK sometimes plays games by asking for the area 'between the curve and the x axis' which is a different concept and would measure distance, not displacement, on a velocity vs time graph.

Is what you said for the other graphs true for 'between the curve and the x axis' also?

 

[MT Headed]

Between the curve and the x axis for an acceleration vs time plot would be speed, not velocity. Velocity is the area strictly _under_ the curve, i.e. anything below the x axis would be considered negative area. I wouldn't worry about area under a displacement/time plot, absence isn't relevant to the mcat though it is an interesting concept.

 

[milski]

Between the curve and the x axis for an acceleration vs time plot would be speed, not velocity. Velocity is the area strictly _under_ the curve, i.e. anything below the x axis would be considered negative area. I wouldn't worry about area under a displacement/time plot, absence isn't relevant to the mcat though it is an interesting concept.

You are right about velocity but the area between the curve and the x-axis (always treated as positive, even below the x-axis) is not speed. It's the cumulative change for velocity which does not have a better name, or at least I'm not aware of it.

A simple example to illustrate that is a graph with the same shape above and below the x-axis. That would give a 0 velocity (which is also 0 speed) but the sum of the positive areas is not 0.

I would not worry about that either in the context of MCAT. At worst, they'll have you deal with a a/t graph which stays in the same quadrant.

 

[ljc]

Don't try to memorize these. Just look at the axes:

The generic formula for slope is rise over run, ie (y-axis)/(x-axis)
The generic formula for area is width times height, ie (x-axis)*(y-axis).

For each of our graphs, this gives:

In a distance (m) vs time (t) graph, your slope is: distance/time, or meters/second, ie velocity.
For that same graph, the area under the curve is distance * time, or m*s.. which is nothing. Meter seconds is not a unit for anything we use.

For velocity vs time, your slope is (meters/second) / seconds, or m/s^2. This is acceleration.
Your area is velocity (meters/second) * time (seconds). (m/s)*s=m, which is displacement.

Acceleration vs time: slope: (m/s^2)/s = (m/s^3), which is nothing
area: (m/s^2) * s = (m/s) = velocity

 

[Temperature101]

I am bumping this thread because I have a question...I came across a few problems about kinematics and graphs in NOVA physics and I missed almost all of them...

For instance, they give a graph of velocity vs time and they ask to graph displacement vs time and acceleration vs time...How do I go about them? Can some explain please?

Edit...I think I got it now. However, if someone wants to provide more explanation, feel free to do so.

 

[circulus vitios]

I am bumping this thread because I have a question...I came across a few problems about kinematics and graphs in NOVA physics and I missed almost all of them...

For instance, they give a graph of velocity vs time and they ask to graph displacement vs time and acceleration vs time...How do I go about them? Can some explain please?

Edit...I think I got it now. However, if someone wants to provide more explanation, feel free to do so.

dx/dt = velocity
dv/dt = acceleration
da/dt = snap or whatever it's called

You're given velocity versus time. To plot acceleration versus time you need to look at the regions of different slope. Look at my crappy drawing and you see there are 6 different regions of slope.

Region #1: Large positive slope.
Region #2: Zero slope.
Region #3: Large negative slope.
Region #4: Zero slope.
Region #5: Large positive slope.
Region #6: Zero slope.

Go over to your acceleration versus time graph.

#1 has a large positive slope. Place a point at some large positive x value.
#2 has zero slope. Move along the time axis to about where region #2 lies and place a zero x value.
#3 has a large negative slope. Move along the time axis to about where region #3 lies and place a large negative x value.
etc.

 

[premed1001]

so is it true for any graph:
the slope of the line is equal to X/Y
and the are under the slope is X*Y?

 

[dudewheresmymd]

so is it true for any graph:
the slope of the line is equal to X/Y
and the are under the slope is X*Y?

what do you mean by X/Y? the slope of the line is delta Y/delta X when (Y is the variable on the y axis and X is the variable on the x axis)

Area under the curve is not necessarily X*Y depends if the graph is a rectangle (in which case it is) if it's a trapezoid or some other figure you have to manually calculate it using the X and Y coordinates.