Simple 1-Dimensional Kinematics Example

Question: Based on the diagram, what is the change in position in meters of an object moving as seen from a time of 2 seconds to a time of 5 seconds?

Answer: 10.5 meters

Explanation: There are many different ways to solve this question.  If you know calculus, you can integrate the velocity function, v = t, from a time of 2 seconds to 5 seconds to get a value of 10.5 meters. Alternatively, since the velocity function is a linear function, you can take the average velocity over the time-frame (^{(2 m/s + 5 m/s)}⁄₂ = 3.5 m/s) and multiply it by the change in time (3 seconds) to get 10.5 meters. Lastly, you can calculate the distance travelled by finding the area underneath the curve from 2 seconds to 5 seconds: this will again be 10.5 meters.