Velocity/Accelration/Displacment all in one question.

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Homework Help Overview

The discussion revolves around a kinematics problem involving a moped's motion, as represented by a velocity versus time graph. Participants are tasked with sketching related graphs for position versus time and acceleration versus time, while also calculating specific values at given times.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between velocity, position, and acceleration, discussing how to derive position from the area under the velocity graph. Some question the need for integration versus calculating areas of geometric shapes.

Discussion Status

There is an ongoing exploration of the equations for velocity across different segments of time. Participants are sharing calculations and questioning assumptions about slopes and intercepts. Some guidance has been provided regarding the integration of velocity to find position, but no consensus has been reached on all aspects of the problem.

Contextual Notes

Participants are working under constraints of homework rules that require sketching graphs by hand and providing numerical values for specific points. There is also a mention of potential confusion regarding the correct interpretation of graph segments and their respective areas.

  • #31
A particle starts from rest and accelerates as shown in Figure P2.11. The divisions along the horizontal axis represent 3.0 s and the divisions along the vertical axis represent 2.0 m/s2.
 
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  • #32
This part should be easier, because it doesn't ask you to plot the graph... yeah, it's similar in concept to the previous one...

What is the area under an a-t graph?
 
  • #33
it should be the v(t).
 
  • #34
veloix said:
it should be the v(t).

yes... generally it would be the change in v(t)... but since here it starts from rest it is v(t) itself...

So what is v(t) at t = 6.0s?
 
  • #35
v(t) at t= 6.0s should be ∫v(t)dt
 
  • #36
veloix said:
v(t) at t= 6.0s should be ∫v(t)dt

Yes, you can just get the area under the curve.
 
  • #37
when i intagrate that i get t^2/2?
 
  • #38
veloix said:
when i intagrate that i get t^2/2?

I don't understand. did you get the velocity at t = 6?

What's the area under the a-t graph from 0 to 6? Just get the area of the rectangle.
 
  • #39
yea it comes out to be 18m/s but it wrong answer.
 
  • #40
veloix said:
yea it comes out to be 18m/s but it wrong answer.

how did you get 18?
 
  • #41
t= 6 v(t)=6^2/2=18m/s
 
  • #42
the area of the rectanlge would 6X2=12
 
  • #43
veloix said:
t= 6 v(t)=6^2/2=18m/s

The a-t graph is just a rectangle... area of a regtangle is length times width = 6*4 = 24.
 
  • #44
oh that's why i got it wrong i had 2 written on my y-axis instead of 4, ugg. so to get the speed at 12s i would get area of each rectangle and add them up.
 
  • #45
veloix said:
oh that's why i got it wrong i had 2 written on my y-axis instead of 4, ugg. so to get the speed at 12s i would get area of each rectangle and add them up.

careful about the 12s though... first get v(12)... take the area above the x-axis, then subtract the area below the x-axis...

That gives v(12), which may be negative... so the speed would be the absolute value of that.
 
  • #46
great that work out perfectly thank you
part c asking for distance this time, the ∫d(t)?
 
  • #47
veloix said:
great that work out perfectly thank you
part c asking for distance this time, the ∫d(t)?

Yeah, plot v(t)... then get the area... you'll need to add all the areas (ie don't subtract areas under the x-axis, just add them)... because the question asks for distance, not displacement...
 
  • #48
i can't draw this plot right I am haveing difficluty.
 
  • #49
veloix said:
i can't draw this plot right I am haveing difficluty.

you should have 3 lines... positive slope... 0 slope (ie horizontal)... and negative slope at the end...
 
  • #50
oh yea that makes sense ty.
 

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