Acceleration, velocity and position

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hello. Im taking university physics and Im having a difficult time with this problem. can someone help me with it? i really appreciate it very much :)

You're testing out a new automobile: starting from rest, you put it through its paces as follows.

a. accelerate for 6.3s at 3.9 m s-2
b. continue to accelerate for 12.2 s at 0.4 m s-2
c. maintain the final speed for 9.6 s
d. hit the brakes--come to a stop in 4.4 s
e. put it in reverse and accelerate backwards for 3.6 s at 2.4 m/m2
f. remain motionless for 6.1 s
g. accelerate uniformly at 2.9 m/s2 for 8.3s

draw three graphs showing position, velocity, and acceleration as functions of time, labeling all values. note that unit conversions are necessary. you may convert to any set of units, as long as they are constant.

from what i understand is to make a graph with the x-axis label as seconds and start from 0 till 13. after, label the yaxis from 0 till 9 m/s2
but its asking 3 graphs! how will i know which is position, velocity and position?
 

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  • #2
collinsmark
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Hello npena29,

Welcome to Physics forums!
You're testing out a new automobile: starting from rest, you put it through its paces as follows.

a. accelerate for 6.3s at 3.9 m s-2
b. continue to accelerate for 12.2 s at 0.4 m s-2
c. maintain the final speed for 9.6 s
d. hit the brakes--come to a stop in 4.4 s
e. put it in reverse and accelerate backwards for 3.6 s at 2.4 m/m2
f. remain motionless for 6.1 s
g. accelerate uniformly at 2.9 m/s2 for 8.3s
Are you sure you got the order of your steps correct? The steps above in red don't make sense in that order.
draw three graphs showing position, velocity, and acceleration as functions of time, labeling all values. note that unit conversions are necessary. you may convert to any set of units, as long as they are constant.

from what i understand is to make a graph with the x-axis label as seconds and start from 0 till 13. after, label the yaxis from 0 till 9 m/s2
The x-axis will need to be longer than 13 seconds. According to the times in your problem statement, something like 0 seconds to 60 seconds would be better.

And all three plots might be positive and negative in the y-axis.
but its asking 3 graphs! how will i know which is position, velocity and position?
Ummm. :uhh: Hmm. The one you label as "acceleration" is the one to plot the acceleration. Plot velocity on the one labeled "velocity"...

Seriously though, perhaps I can reword what you are supposed to be doing in this exercise.

Start with acceleration. The acceleration of each segment is given to you in most of the above steps in the problem statement. You'll have to do a little calculation to find the acceleration in the "hit the brakes--come to a stop" step. But once you find that, plotting the acceleration graph should be fairly simple. (Hint: if you do it right, the curve plot should just have straight-line "rectangle" shapes in it. And it will be discontinuous -- sometimes immediately jumping from one y-axis value to completely different one. But the slopes of all the lines will be 0, except at the points of these discontinuities. That's because we are assuming that within each segment, the acceleration is uniform.)

Then move on to the velocity graph. Use the same time scale (for the x-axis) that you did in the acceleration graph. But the rest of this velocity plot is trickier. The y-component of the velocity curve, at any point in time, is the total area under the acceleration curve from 0 to that particular point in time (keeping in mind that any area "below" the x-axis in the acceleration curve is treated as negative area). (Hint: if you did it right, this curve will only contain straight lines. But unlike the acceleration curve, some lines will be slanted [i.e. have non-zero slopes]. Also unlike the acceleration plot, this curve should be continuous [if you have any discontinuities in the velocity plot, something went wrong].)

Do the same thing with the "position" plot, except use the velocity graph for the area under the curve. [Hint: if you did it right, this plot really looks like a curve. The plot is continuous and doesn't even have any "edges" in it. 'Just one smooth curvy curve.]
 

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