How to Calculate Velocity as a Function of Time

The kinematic equations in physics are four really nifty formulas to find 1) velocity as a function of time, 2) velocity as a function of position, 3) position as a function of velocity and time, and then 4) position as a function of time. Use the following steps to calculate the kinematic equation to calculate the first physics equation, velocity as a function of time. Read on to learn more.

Difficulty:

Moderately Challenging

Instructions

1. Calculate velocity as a function of time for constant acceleration using the formula:
   "v (final) = v(initial) + a (average)t." In English that is final velocity (v) equals the initial velocity (v) plus the average acceleration (a) multiplied by time (t).

2. Use this physics equation when you have the initial velocity and the particle or object you are calculating for is under constant acceleration. Usually this is for free-falling objects close to the earth where gravity is the standard "9.8 m/s^2."

3. Understand that this velocity equation comes from the formula for average acceleration, which is "a = [v(final) - v(initial)]/[t(final) - t (initial)]." In this equation again a equals average acceleration, v equals velocity and t equals time.

4. Simplify this equation to just one t (time) by using t (initial) at 0. So now the equation reads: "a = [v (final - v (initial)]/t."

5. Do a little algebra rearrangement on "a = [v (final) - v (initial)]/t" and you get the kinematic equation for velocity as a function of time as above: "v (final) = v (initial) + a (average)t."

6. Employ this velocity equation for one-dimensional motion at constant acceleration such as a free-falling object.

7. Make use of this formula as the first step and first equation in applying the kinematic equations in physics for motion in a straight line in constant acceleration.