Finding the x component from a velocity vs. time graph

In summary, Bella walks in a straight line with the positive direction to the right. Her velocity changes along the x-axis according to the equation v = \Delta x/\Delta t. The slope of the line is the acceleration.
  • #1
ran
3
0
First-time poster here.

Homework Statement



A little cat, Bella, walks in a straight line, which we shall call the x axis, with the positive direction to the right. As an observant scientist, you make measurements of her motion and construct a graph of the little feline's velocity as a function of time.

Find the x component of Bella's velocity at t = 2.00 s. (in m/s)

Find the x component of Bella's velocity at t = 7.00 s. (m/s)

What is the x component of her acceleration at t = 2.00 s? (in m/s^2)

What is the x component of her acceleration at t = 6.00 s? (m/s^2)

What is the x component of her acceleration at t = 7.00 s? (m/s^2)

For some reason, I can't get the image to show up. Here is the link to it: http://img32.imageshack.us/img32/4815/1012297.jpg

Homework Equations



v = [tex]\Delta[/tex] x/ [tex]\Delta[/tex] t
a = [tex]\Delta[/tex] v/ [tex]\Delta[/tex] t

The Attempt at a Solution



The graph is velocity versus time with a negative slope, and the slope is the acceleration. I have no clue as to how I should go about finding the x-component of the velocity in m/s. There's no angle given, only the graph. As for the acceleration questions, I found the the slope of the change in velocity over the time (according to the values on the graph) and the answers were also incorrect. Any hints?
 
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  • #2
In what direction is she moving?
So what should you do to get x-component?[It's the easiest thing to do in the world :P]
 
  • #3
If I'm not mistaken, your graph shows the x-component of the velocity against time - so you should be able to simply read from the values from the graph. You also must be careful as the units on the graph are cm/s - and the question is asking for m/s.

As for the acceleration, it looks as though you've done the right thing - but once again make sure you convert from cm/s^2 to m/s^2.
 
  • #4
its difficult to acquire x components from the graph so I believe that an relevant equation would be:

V = V(initial)+at

where a is the slope of the graph (which, since the line is straight, is known to be constant throughout).
 
  • #5
Hello everyone,

I appreciate the responses. After getting the answers wrong yet again, I found a similar problem via Google. I was (sort of) on the right track by reading the values off of the graph.

The only problem was that the answers require precision down to the decimals (i.e. the velocity for t = 2 s was 5.33 cm/s). That's obviously hard to see on such a tiny graph. The average acceleration is roughly 1.3 cm/s^2, so I would have been better off doing this calculation first, then determining the change in velocity for each point in time (just as you said, bruiser).
 

Related to Finding the x component from a velocity vs. time graph

1. How do you find the x component from a velocity vs. time graph?

The x component can be found by looking at the horizontal axis of the graph, which represents time, and finding the corresponding point for the desired time. Then, you can look at the vertical axis, which represents velocity, and find the corresponding point for the velocity at that time. The x component is the distance traveled at that specific time.

2. What unit is used for the x component in a velocity vs. time graph?

The unit for the x component can vary depending on the graph and the problem being solved. However, it is typically measured in meters (m) or kilometers (km) for distance, and seconds (s) for time.

3. Can you find the x component if the velocity vs. time graph is not a straight line?

Yes, you can still find the x component even if the graph is not a straight line. However, it may require more calculations or measurements to accurately determine the distance traveled at a specific time.

4. How does the slope of a velocity vs. time graph relate to the x component?

The slope of a velocity vs. time graph represents the rate of change of velocity over time, also known as acceleration. The x component, on the other hand, represents the distance traveled at a specific time. The slope can be used to calculate the x component by multiplying it by the time interval.

5. Is it possible to find the x component if the velocity vs. time graph is not labeled?

It may be difficult to find the x component if the graph is not labeled. However, if the graph is a standard velocity vs. time graph, with velocity on the y-axis and time on the x-axis, then it is still possible to determine the x component by following the steps mentioned in the first question.

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