When the initial and final velocities are u and v, respectively, a is the acceleration and t the time, then

The relationship between these variables can be described by the first equation of motion, which is:

v = u + at

This equation states that the final velocity (v) of an object is equal to its initial velocity (u) plus the product of its acceleration (a) and the time (t) for which it has been accelerating.

Here's a step-by-step breakdown:

1. Start with the initial velocity (u). This is how fast the object is moving at the start of the time period you're considering.

2. Multiply the acceleration (a) by the time (t). This gives you the change in velocity due to the object's acceleration over this time period.

3. Add the result from step 2 to the initial velocity. This gives you the final velocity (v) of the object at the end of the time period.