# 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.*

Posted in Transportation Breadth and tagged acceleration and deceleration, civil pe, transportation breadth. Bookmark the permalink. Leave a Comment.

## Leave a Comment

## Comments (0)