Question

What is the formula for distance from a changing velocity?

Answer 1

If the velocity is changing at a constant rate, meaning that the acceleration is constant, we may derive the formula as follows.

The velocity `v` varies linearly with time and is given by the relation `v(t)= v_0 + at` where `v_0` is the initial velocity and `a` is the acceleration.

We know that distance is the product of average velocity and time, and the average velocity is the average of the initial and final velocity. In mathematical terms,

`v_{avg}= \frac{v_0 + v}{2} = \frac{v_0 + (v_0 + at)}{2} = v_0 +\frac{at}{2}`

Simply multiply that by time `t` to get the distance `s`.

`s = (v_0 + {at}/2)*t = v_0 t + 1/2 at^2`