# Acceleration and Deceleration

Acceleration is measured in velocity change per second, so miles per hour per second (mphps), feet per second per second (fpsps or fps/s) etc. Deceleration is negative acceleration, so I probably won’t use that term from here on out and simply stitch with acceleration.

If you are starting from zero with an acceleration of 3 fps/s, your velocity will increase by 3 for every second from then on. So 0, 3, 6, 9, 12 etc.

There is one equation relating velocity(v) and acceleration(a):

$$v_f = v_0 + at$$

Use this equation for any problem with initial and final velocity, and acceleration.

There are two equations for distance traveled (x) that involve acceleration(a). The first depends on time elapsed (t) and the second depends on a final velocity ($$v_f$$). Both depend on an initial velocity ($$v_0$$):

$$x = x_0 + v_0t + \frac{1}{2}a t^2$$

Use this equation for problems with acceleration, distance, initial velocity, and time.

and also this one, which is a solved differential equation relating velocity and acceleration:

$$! v_f^2 = v_0^2 + 2ax$$

here it is rearranged for distance travelled:

$$x = \frac{v_f^2 – v_0^2}{2a}$$

Use this second equation for problems with acceleration, distance, initial velocity, and final velocity. 