The city schoolPHYSICS

Saqib javeed April12,2011

The Meaning of Slope for a v-t Graph

• As discussed in the previous part of Lesson 4, the shape of a velocity vs. time graph

• reveals pertinent information about an object's acceleration. For example, if the

• acceleration is zero, then the velocity-time graph is a horizontal line (i.e., the slope is

• zero). If the acceleration is positive, then the line is an upward sloping line (i.e., the slope

.

Consider a car moving with a constant velocity of +10 m/s. A car moving with a constantvelocity has an acceleration of 0 m/s/s.The velocity-time data and graph would look like the graph below. Note that the line onthe graph is horizontal. That is the slope of the line is 0 m/s/s. It is obvious that in thiscase the slope of the line (0 m/s/s) is the same as the acceleration (0 m/s/s) of the car.

So in this case, the slope of the line is equal to the acceleration of the velocity-time graph.Now we will examine a few other graphs to see if this is a principle which is true of allvelocity vs. time graphs.

The velocity-time data for this motion show that the car has an acceleration value of 10m/s/s. The graph of this velocity-time data would look like the graph below. Note that theline on the graph is diagonal - that is, it has a slope. The slope of the line can becalculated as 10 m/s/s. It is obvious once again that the slope of the line (10 m/s/s) is thesame as the acceleration (10 m/s/s) of the car.