How Accurate is Your Speed-Time Graph?

[Anzas]

my physics teacher made this graph and asked us to draw the graph of the speed as a function of time
heres what i got tell me what you think...

 

[HallsofIvy]

Looks good. The "distance vs time" graphs (I assume that's what they are- you didn't say so) are made of straight line segments so the corresponding speed is a constant, the slope of the distance graph and the speed vs time graph is a horizontal straight line for that time interval.

 

[Anzas]

that teacher of my, called the speed/time graph a function, the speed is not even defined at a few points because the acceleration is infinite

 

[DaveC426913]

Can you elaborate? Is your prof calling it a time machine? or are you?

Unless I misunderstand, it seems that you are splitting hairs. This is a sketch, designed to show the relevant aspects of the data - the relationship between changing velocity and position. The accelerative aspects are made deliberately trivial. Technically, yes, the slope would be defined, and in reality would not be vertical.

 

[Anzas]

i just call it a time mechine as a joke (because the acceleration at a few points is infinite) i personally think its a mistake giving such a graph in class all it does is make people confused on how it is possible that the acceleration is infinite.

 

[HallsofIvy]

The point about "the speed is not even defined at a few points because the acceleration is infinite" refers to the points at which the distance graph has "corners". The velocity itself is not defined there and the graph "jumps" from one value to another.

 

[joyful55]

Well, let's just say that these graphs are on an ideal case where velocity is able to switch to any value at any point of time which is in fact irrational.

 

[DaveC426913]

You are clever enough to see that the graph is too simplistic for your own level of understanding. Not everyone will grasp the concepts quite so quickly.

The question at hand is, what treatment best teaches the student body the concepts intended?

If the teacher is trying to teach the relationship between velocity and distance, an idealized graph will do that, without obfuscating the issue with real - yet contextually irrelevant - facts.