Calculating velocity and acceleration from a position-time graph

[alexandria]

Homework Statement

Homework Equations

acceleration equation:
a = v2 – v1 / t2 – t1

The Attempt at a Solution

Can someone please tell me if my answers make sense. Thanks in advance :)[/B]

21.

22.
to calculate the velocity, i determined the slope of the tangents, postioned at 0.50s, 0.75 s, and 1.00 s

Using this information, i created a velocity time graph for the orange

Acceleration:

a = v2 – v1 / t2 – t1

a = 8.5 m/s (down) – 6.7 m/s (down) / 1.00 s – 0.75 s

a = 7.2 m/s2 (down)

 

[haruspex]

Not bad, but which of all the available datapoints for velocity should be the most reliable?

 

[alexandria]

what do you mean? are you referring to the velocity i calculated in my time-velocity data table? and what do you mean by most reliable? arent they all reliable?

 

[haruspex]

what do you mean? are you referring to the velocity i calculated in my time-velocity data table? and what do you mean by most reliable? arent they all reliable?

They're not wonderfully reliable because you are drawing tangents by eye and finding the velocities from their slopes. I can see, for example, that your tangent at 0.5s is a bit too steep.
There is one completely reliable velocity that you have not used. You do not even have to draw a tangent to find it!

 

[alexandria]

i don't understand :P

 

[haruspex]

i don't understand :P

Which bit don't you understand, the inaccuracy inherent to the method you have been told to use to find velocities, or what data point you have not used?

 

[alexandria]

both
i was just told to draw tangents and then calculate the slope of each tangent to determine the velocity
here's an example from my lesson:

 

[haruspex]

i was just told to draw tangents and then calculate the slope of each tangent to determine the velocity

Yes, I understand that, but you must realize that drawing tangents by eye like that is open to substantial error. The tangent you drew at 0.5s looks to me more like the tangent at 0.55s.
Since you are following a worked example, I suppose you cannot do much better than that. But had I prepared the example I would have taken the velocity at time 0 as an obvious known value. Note that using that value together with your t=1 tangent gives a rather more accurate value for g.

 

[alexandria]

ok i understand, should i fix the tangent at 0.5 s, will that make it more accurate?

 

[haruspex]

ok i understand, should i fix the tangent at 0.5 s, will that make it more accurate?

Yes, a bit.

 

[alexandria]

ok thank you.