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Phy 231
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Angular Velocity Questions 3/4
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3. Find the area and slope of a v vs. t trapezoid with ‘graph altitudes’ v0 and vf, and width `dt. Using `dx for the change in position and a for the change in clock time, express your results in the form of two equations. The quantities in your equations will be v0, vf, `dt, a and `dx, though neither equation will contain all of these quantities. The quantities `dt and vf, however, will be common to both equations (as will v0). Treating your two equations as simultaneous equations, what steps do you take to eliminate `dt from and what equation do you get? Repeat, this time eliminating vf from your two equations.
4. How can you reconcile the results obtained in the preceding two questions? That is, how can you get each set of equations from the other?
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I understand the first part of question 3, but do not get the 2nd part. I don't understand the part about eliminating vf and dt form the equations.
Since I don't understand 3 of course 4 also since it is a follow up.
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How do I go about getting the equations without vf, and without dt?
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You haven't indicated what the equations you are looking at are.
I'll assume you got them right. In which case the equations are
a = (vf - v0) / `dt
and
`ds = (vf + v0) / 2 * `dt
Solve the first equation for `dt, substitute the result for `dt in the second, and simplify. What do you get?
Then solve the first for vf and substitute the result for vf in the second. What do you get?
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