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Evaluating Velocity and Acceleration

Hi, please give the step by step solutions so I can see how you got the answers and understand it.

The graph on the page is a velocity versus time graph. The time is in seconds. The graph has points at (0,20),(5,40),(10,60),(15,80),(15,60),(15,40),(15,20),(15,0),(15,-20),(15,-40),(20,-40), and then the next point is approximately (21.5, -25).

The following question go with the graph above.

1) Based on the graph of velocity versus time, what is the acceleration at t=10 seconds?
2) If the initial position of the object is 50 meters at t=0 seconds, what is the position of the object at 30 seconds?
3) What was the average velocity of the object from zero to 30 seconds?
4) Select all the times when the acceleration is positive.
a) From 0 till 15 seconds
b) From 15 till 20 seconds
c) From 25 till 30 seconds
d) From 25 till 30 seconds
5) At what time is the object the furthest away from its starting point at t=0?

Solution Preview

Note: The points you listed as given for a velocity/time graph are:
(0, 20), (5, 40), (10, 60), (15, 80), (15, 60), (15, 40), (15, 20), (15, 0),
(15, -20), (15, -40), (20, -40). See attachment for the graph showing
these points.

The first five points you listed are ok. They are on a straight line from
(0, 20) to (15, 80).
With these points, the acceleration is the slope, (velocity change over time change) of this line, namely: a= (80 m/s - ...

Solution Summary

This solution provides a step-by-step explanation of how to answer each part of this question. As well, a pdf attachment is provided which has the accompanying graph mapped out.