How to calculate distance travelled from a speed-time graph

2(g) calculate the area under a speed-time graph to determine the distance traveled for motion with uniform speed or uniform acceleration.




Calculating Distance traveled a from speed-time graph

Speed time-graphs are mostly meant to be as velocity-time graphs in the CIE exams. What speed time graphs basically show us is the speed of an object at a particular time.

But from a speed time graph, we can also obtain the following quantities.

• Distance
• Uniform Acceleration and Deceleration

Distance from speed time graphs


 
We know that speed = distance/time. From this equation, we can derive the formula for distance which is = speed * time. Now, always remember one thing. In a speed time graph of an object, the distance traveled by that object is always the area under the graph. By that, it means that the area under the figure that is formed as a result of the speed-time graph is the distance covered by that body.

You might wonder why this is so. This is due to the fact that the area under the graph is actually the product of the speed and time, which equates to the distance which we needed in the first place. Now in the following figure, lets consider the red trapezium. We can calculate the area of the trapezium by the formula, 1/2 sum of parallel sides* height. That is 1/2 (3+10) * 8. The answer is 52m. This is the total distance traveled by the body in the following speed time graph during the 10s.