Afstandsprobleem

The distance problem finds how far an object has traveled using velocity measured at different points in time.

When velocity varies, the total distance can be approximated by adding small displacement intervals, each showing motion over a short time step.

For example, in a race, a runner accelerates steadily during the first three seconds. Velocity measurements taken every half-second show the speed increasing from 0 to 6.2 meters per second.

These measurements are used to estimate the total distance by dividing the velocity–time graph into half-second rectangles for the lower sum and the upper sum.

The lower estimate uses velocities at the left endpoints of each time interval. Multiplying each of these velocities by the half-second time step and summing the individual results gives 10.55 meters.

On the other hand, the upper estimate uses right endpoint velocities. Multiplying each of these by the time step and adding gives 13.65 meters. The actual distance lies between these two estimates. Increasing the number of measurements leads to a more accurate result.

With infinite measurements, the distance equals the area under the curve, shown by the integral of velocity over time.