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One method was tangents and the other was average velocity at half-time. Could you please explain these methods to me? (in terms of graphical use)

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- Thread starter rum2563
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- #1

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One method was tangents and the other was average velocity at half-time. Could you please explain these methods to me? (in terms of graphical use)

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I'm guessing that what you mean is, when you plot displacement vs. time on a graph, the tangent at any point will have a slope that is the instantaneous velocity.

I don't know what you mean by the other method. There are tons of ways to find a velocity, literally hundreds, it is all situational.

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One method was tangents and the other was average velocity at half-time. Could you please explain these methods to me? (in terms of graphical use)

I feel I should point out that finding the average velocity of an object will

[tex]s = s_{0} + v_{0}t + \frac{1}{2}at^2[/tex]

[tex]v = v_{0}t + at[/tex]

[tex]v^2 = v_{0}^2 +2a\left(s - s_{0}\right) [/tex]

If an object experiences a constant acceleration, then these equations can be used to compute the instantaneous velocity for an object given the elapsed time or the displacement.

Incidentally, there is a certain theorem in mathematics, the Mean Value theorem which says that given some time interval, a moving object's instantaneous velocity will be equal to its average velocity over the entire interval at

- #6

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One method was tangents and the other was average velocity at half-time. Could you please explain these methods to me? (in terms of graphical use)

The 2nd method can be applied only when the acceleration a is constant. Then the velocity is calculated as :

v=vo+at

and if you calculate the velocity at midpoint of the to=0 and t1, you have:

vad = vo+(a*t1)/2= 1/2(2vo+a*t1) = 1/2[vo+(vo+a*t1)] =1/2(vo+v1)

That is the average of vo and v1.

Where:

vad : instant velocity at midpoint

t1 : the time when you have velocity v1

Or more simply, you can graph the v against time, there will be a triangle.

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HallsofIvy

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Ah, excellent! Haiha has it exactly. I was wondering myself what your teacher could be talking about but that has to be it.

Although, however, it is going the other way. If an object has**instantaneous** velocity v_{0} at one point and instantaneous velocity v_{1} at another point **and** has constant acceleration then its average velocity between those two points is (v_{1}+ v_{2})/2. Of course, if you know the velocity at one point and the average velocity, you can use that to find the instantneous velocity at any point (still with the assumption of constant acceleration).

Although, however, it is going the other way. If an object has

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