Given position vs time graph, find velocity?

In summary, the conversation discusses the calculation of a bicyclist's velocity at different times using the slope equation. It is determined that the velocity at t=10s is 7.5, but the answer needs to be rounded to two significant figures. It is also noted that when the position of the cyclist does not change, the velocity is 0, and when the position changes in a negative direction, the velocity is negative. The conversation also explores the concept of negative gradients and how they indicate a change in direction.
  • #1
skysunsand
39
0

Homework Statement



Given the graph in the uploaded screenshot, what is the bicyclist's velocity at t=10s?

Homework Equations



I have been trying to do a slope equation? Rise/run.

The Attempt at a Solution



Tried to do slope equation. Looks like 75/10, which would be 7.5, but that answer is incorrect. Why? It wants to two sig figs, and that is two sig figs...I also have no clue what to do if t= anything else, like 25 or something. Is there a different equation for that? I'm so lost. :(
 

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  • Screen shot 2011-08-23 at 10.10.50 PM.png
    Screen shot 2011-08-23 at 10.10.50 PM.png
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  • #2
rise over run wouldn't be 75/10. it starts at 50 and then moves to 75. so the change in distance is 75-50=25. so rise over run is 25/10
 
  • #3
remember speed is distance traveled/time taken. when time= 0, its position isn't zero like you assumed. It's position is 50. And then in 10 seconds its position is 75. So the distance traveled is 25. So s=d/t, where d=25 and t=10seconds.
 
  • #4
Would I do the same then, for an amount like 25 or 35? Or do I say 25 would be 0, since there is no slope there, and then 35 would be a negative number, because the slope is going downward?
 
  • #5
if t=25, all you need to do is look at the graph. what is happening at t=20? position is 100. now take t=25. position is still 100. what does that mean? in 5 seconds the position of the cyclist has not changed which means he is stationary. not moving so velocity is zero. The formula can also be applied. s=d/t. between 20 and 25 seconds. distance traveled is zero in a time frame of 5 seconds. so s=0/5 = 0. which is the same as saying rise over run. Between 20 and 30 would be the same, distance traveled between 20 and 30 seconds is zero in a time frame of 10 seconds so s=0/10=0. At t=35, the slope has changed. at t= 30 seconds position was 100 but now at t=35, the position is 50 again. So distance traveled is final distance minus the initial distance so 50-100=-50. And that has occurred in a time frame of 5 seconds. so again s=d/t, -50/5=-10 so velocity is -10.

That is why it has a negative gradient. So essentially, if the position at t=0 is 50 and then at t=25 is 100 and then at t=35 is 50 again it means he is going backwards. he has turned around at t=30 and is heading back
 
  • #6
thanks a lot that help me a lot too. I fully understand it now
 

1. What is a position vs time graph?

A position vs time graph is a visual representation of the relationship between an object's position and time. The horizontal axis represents time, while the vertical axis represents position. The slope of the graph at any given point represents the object's velocity at that moment.

2. How do I find velocity from a position vs time graph?

The velocity can be found by calculating the slope of the position vs time graph at a specific point. This can be done by finding the change in position (Δx) over the change in time (Δt) between two points on the graph. The formula for velocity is v = Δx/Δt.

3. What does a positive slope on a position vs time graph indicate?

A positive slope on a position vs time graph indicates that the object is moving at a constant positive velocity. The steeper the slope, the greater the velocity.

4. How can I determine the direction of an object's motion from a position vs time graph?

The direction of an object's motion can be determined by the slope of the position vs time graph. A positive slope indicates motion in the positive direction, while a negative slope indicates motion in the negative direction.

5. Can a position vs time graph show changes in acceleration?

Yes, a position vs time graph can show changes in acceleration. This is represented by the curvature of the graph. A curved graph indicates that the object's velocity is changing, and therefore, it is accelerating.

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