Speed-Time Graphs

:: | Instantaneous Speed | ::

Like distance and time, speed and time can also be placed visually on a graph as well. A speed -time graph that has a slope greater than zero shows an object accelerating, graphs that shows a straight means a constant speed is being kept, and a negative slope means the car is decelerating. The steeper the slope, the faster it is either accelerating or decelerating.

This page will pose a new way of showing acceleration using a graph. Acceleration is the change in speed over time. Usually in a speed-time graph the speed is represented as the change in y (y) or the y-axis. The time is represented as the change in x (x) or the x-axis. The equation of the slope is still defined as the change in y divided by the change in x

Slope = (y/x)

To calculate the Acceleration from a speed time graph you must calculate the slope the same way you would fine the average speed from a distance-time graph. (click here)

What does the area under the line mean?

The area under the slope represents the total distance. Using mathematical formulas, you can find the area under the line. Normally shape in which the area can be measured from willl only form a triangle or a square, or both.

This theorem still proves the area under a speed-time graph equals the distance travelled during that time interval.

Sample 2

Using the above graph you can calculate the area. (in meters)

i) Divide the slopes in to geometric shapes if necessary

ii) Decide what formulas to use

 Triangle Area = (Base x Height) / 2 Sqaure Area = Base x Height

iii) Calculate the areas

 Triangle Area = (Base x Height) / 2 (4 x 5) / 2 = 10m Sqaure Area = Base x Height (9-4) x 5 = 25m