Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

The integral of a vector

Starting from rest, a flying saucer of mass m is observed to vary its propulsion with mathematical precision according to the equation

(The aliens inform us that the numbers 42 and 137 have a special religious significance for them.) Find the saucer's velocity as a function of time.

From the given force, we can easily find the acceleration

The velocity vector v is the integral with respect to time of the acceleration,

and integrating component by component gives

where we have omitted the constants of integration, since the saucer was starting from rest.

Last Update: 2009-06-21