Differentiaalvergelijkingen: probleemoplossen

A safety check on a ship uses a heavy test weight. The weight is lifted and then released to study how air resistance affects motion. Once it is let go, the weight starts from rest and falls through the air.

Gravity pulls it downward, while the air pushes upward against its motion. According to Newton’s Second Law, the change in speed depends on the net force.

Combining these forces gives a differential equation that links acceleration to speed. Dividing the equation by mass gives a simpler form.

Defining the ratio of the drag constant to the mass as the constant b makes the differential equation easier to separate.

Integrating the equation and rewriting it to find the equation for velocity as a function of time gives an exponential equation. Using the initial velocity of zero helps find the remaining constant in the solution.

As time increases, the velocity approaches a constant value known as terminal velocity. With a weight of 10 kilograms and a drag constant of 2 newton-seconds per meter, the model predicts a terminal velocity of 49 meters per second.