Supposing d(t) is known to have value d,
what procedure will find the time t at which
this happens?

Explanation:

This question assumes uniformly accelerated motion, for which the distance d a particle travels in time t is given by the general equation:

That is a quadratic equation, where the independent variable is the time .

Thus, the procedure that will find the time t at which the distance value is known to be D is to solve the quadratic equation for .

To solve it you start by changing the equation to the general form of the quadratic equations, rearranging the terms:

Some times that equation may be solved by factoring, and always it can be solved by using the quadratic formula:

Where:

That may have two solutions. Some times one of the solution makes no physical sense (for example time cannot be negative) but others the two solutions are valid.

a and b sometimes have a positive value