Mission KG8 Slope and Area of a Velocity-Time Graph

Getting your Trinity Audio player ready...

Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

This velocity-time graph depicts the motion of an object. Use the graph to determine the displacement (in meters) of the object during the entire 5.0 seconds (OR 4.0 seconds OR 8.0 seconds).

Velocity-Time Graphs:
Velocity versus time graphs represent changes that occur in an object's velocity with respect to time. The slope of the line is the acceleration (change in velocity divided by the change in time) of the object. The area under the line (between the line on the graph and the time axis) is the displacement of the object.

Success on this question will involve accurately calculating the area between the line on the graph and the time axis for the first 5.0 seconds (OR 4.0 seconds OR 8.0 seconds). The shape of the region between the line and the time axis is a trapezoid. The area of a trapezoid can be calculated using the information and formulae in the Math Magic section below. Take your time dividing the trapezoid into the more convenient rectangle and triangle. Be accurate with your readings of the height and the base and enter your answer to at least the second decimal place.

A trapezoid can be thought of as a triangle resting on top of (or beside) a rectangle. The total area of the trapezoid can be determined quite easily by dividing it into a rectangle and a triangle and summing the areas of each of these smaller shapes. The area (A_rect) of a rectangular shape can be determined from knowledge of the height (h_rect) and the base (b_rect) of the triangle.

A of Rectangle = base • height
A_rect= b_rect• h_rect

The area (A_tri) of a triangular shape can be determined from knowledge of the height (h_tri) and the base (b_tri) of the triangle.

Area of Triangle = 0.5 • base • height
A_tri= 0.5 • b_tri• h_tri