Video Transcript
The figure shown is a velocity–time graph for a body moving in a straight line with an initial velocity of 10 meters per second. Determine the total distance covered by the body, given that it came to rest 100 seconds after it started moving.
We can see from the graph that the body’s velocity increased from 10 meters per second to 35 meters per second in the first 10 seconds. It then traveled at a constant speed for a further 20 seconds before decelerating to rest after 100 seconds. In any velocity–time graph, we can calculate the distance covered by working out the area underneath the graph. We can make this calculation easier by splitting our area into different parts. In this question, we have split it into a trapezoid, or trapezium, a rectangle, and a triangle. However, we could’ve split it into two trapezoids, otherwise known as trapeziums.
We can calculate the area of any trapezoid by adding the lengths of the parallel sides, dividing by two, and then multiplying by the perpendicular height. The parallel sides have lengths 10 and 35, and the height between them is also 10. This gives us an answer of 225. The distance covered in section A is, therefore, 225 meters. Shape B is a rectangle, and we calculate the area of a rectangle by multiplying the length by the width or the base by the height. 20 multiplied by 35 is equal to 700. So, the distance covered in this part of the graph is 700 meters.
Shape C is a triangle. And we can calculate the area of a triangle by multiplying the base by the height and dividing by two. We multiply 70 by 35 and then divide this answer by two, giving us 1225. The total area under the graph is, therefore, equal to 225 plus 700 plus 1225. This is equal to 2150.
The distance covered by the body is 2150 meters, or 2.15 kilometers.
