course phy121
We plot the information on a graph of time vs. velocity. We can then use the area under the line to determine the change in position of the object. Simple division of Vf (final velocity) minus Vi (initial velocity) and divide the differece by total time duration will give you the average velocity of the object. Apply this to the graph will allow you to calculate the velocity at any point along the line.
In terms of the meanings of altitudes, area, slope and width, how does a velocity vs. clock time trapezoid represent change in position and acceleration?
Its area represents the distance traveled in the particular time interval, while the slope represents the change in acceleration.
To answer these questions you need to specify the meaning of the average 'altitude' of the trapezoid and its 'width', then figure out what it means to multiply the first quantity by the second. As I believe you understand, the average 'altitude' of a v vs. t trapezoid represents the average value of v, and the 'width' represents the change in the clock time, so that the area, representing the product of these two quantities, therefore represents the average displacement.
Similarly the 'rise' between the two points represents the change in the velocity and the 'run' represents the change in the clock time. The slope therefore represents change in velocity / change in clock time = average rate of change of velocity with respect to clock time = average acceleration.