course phy 201
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If we know the initial and final velocities over some time interval, and if the rate which velocity changes is constant, then how do we calculate the displacements over a series of time subinte
To find the displacements over a series of time subintervals you would first calculate the displacement in each of the time intervals. You would do this by finding the average velocity and then finding the time interval. You would then multiply these to together to get the area of the trapezoid. Then to find the s you would add the change in displacements for each of the intervals.
Video 14
Having calculated displacements over all specified subintervals, how do we obtain the total distance moved from the initial clock time up through the end of each subinterval?
You have the displacements for each time interval and then you add that displacements for each of the intervals. Like a running tab.. if you had 5 intervals you would add interval 1 +2 = answer and then answer + 3 = new answer and then new answer +4 = even newer answer then the even new answer + 5 will equal the total distance moved from the initial clock time up through the end of each subinterval.
How do we construct a position vs. time graph from a velocity vs. time graph?
You can calculate the positions for each time interval from the velocity vs time graph. You can then plot these points. If you wanted to check to see if you math was right and that your graph is correct you could find the slope at a point on the graph and see if it matches the velocity on the other graph.
Video 15
How do we symbolically and graphically represent the calculation of the displacement corresponding to a given initial and final velocity over a given time interval?
The area of the trapezoid is the time interval * the average velocity. So you would take the final velocity and add it to the initial velocity and then divide it by 2.They you would find the time interval and multiply that by the average velocity.
How do we know when to subtract and when to add the initial in final velocities in calculating average rates of velocity change and displacements from initial and final velocities and time interval?
If you subtract the velocities you would be finding the change in velocity and then divide it by two would not make since. If you were to add the velocities when finding the slope that would not make since either.
To calculate the average rate you would add the velocities and divide by 2
to calculate the change in velocity you would subtract.
to calculate the slope you would subtract the velocities and then divide by the time interval
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Your answers are good. Good insight.
Let me know if you have questions.