What is the formula for distance from a changing velocity?

1 Answer
Oct 6, 2014

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#