**Acceleration: Change in Velocity Over Time**

**Acceleration** is describing how velocity changes. Learn more about acceleration and picking the right equation used in physics problems. In the next lesson we will cover the acceleration due to gravity.

With acceleration velocity changes so never use variable **v** since it means constant velocity. Therefore, **v _{i}** represents

**initial velocity**and

**v**represents the

_{f}**final velocity**.

### Acceleration Equation Variables

Name |
Variable |
Unit |
Unit Abbreviation |

Initial Velocity or Initial Speed |
v_{i} |
meters per second | m/s |

Final Velocity or Final Speed |
v_{f} |
meters per second | m/s |

Time |
t | seconds | s |

Acceleration |
a | meters per second squared | m/s^{2} |

Displacement or Distance |
X | meters | m |

**Most Common Acceleration Equation**

The most common acceleration equation is it's definition. **Acceleration equals change in velocity over time**.

With change in velocity expanded out below:

The following acceleration equations can be used to answer any accelerated motion problems. Observe the variables in our animated videos.

**v**_{f} = v_{i} + at

_{f}= v

_{i}+ at

Final velocity equals the initial velocity plus the acceleration times the time. Common version of this equation can be seen below.

**x = v**_{i}t + ½ at^{2}

_{i}t + ½ at

^{2}

Displacement equals initial velocity times time plus one half acceleration times time squared.

**v**_{f}^{2}=v_{i}^{2} + 2ax

_{f}

^{2}=v

_{i}

^{2}+ 2ax

Final velocity squared equals initial velocity squared plus two times acceleration times displacement.

**x = ((v**_{i} + v_{f})/2)t

_{i}+ v

_{f})/2)t

Displacement equals the sum of initial velocity and final velocity divided by two and then multiplied by time

**Picking your acceleration equation**

Once you determine an object is speeding up or slowing down in a problem and you are given three variables and one to solve for, you know you have to pick from the acceleration equations.

Example question as you walk through the steps. **How fast** was Chancellor running **after** starting **from rest** and **accelerating at 4.5 m/s ^{2 }**for

**2 seconds**?

**Step one**: read the entire problem**Step two**: pick out the unknown the question is asking you to solve for and add it to a givens list. (example:**v**)_{f}= ?**Step three**: pick out the variables given in the equation. (example:**v**,_{i}= 0 m/s**a= 4.5 m/s**,^{2}**t= 2s**)**Step four**: figure out which variable is missing (example:**x is missing**)**Step five**: pick the one equation that**does not have**that missing variable (in this example:**v**)_{f}= v_{i}+ at

**Note**:

- The variable you are solving for will not always be the first thing before equals in the equation, you will likely have to do algebra. For example I might be using this equation (v
_{f}= v_{i}+ at) to solve for time and not just final velocity. - If the variable in the equation is squared you will have to take the square root so solve for only the variable at some point. Example, if you use v
_{f}^{2}= v_{i}^{2}+ 2ax. to solve for v_{f }you need to make v_{f}^{2 }become v_{f }by taking the square root of it. - If you have more than four total pieces of information, one unknown and more than three knowns, you can choose multiple equations to get the same answer.
- If you need additional assistance with picking or rearranging the equations get more help through video tutorials at
**Holdensclass.com**following this link.

**Example Problems**

**1. How fast is Tommy Running after starting from rest and accelerating at ****2 m/s**^{2} for three seconds?

**2 m/s**for three seconds?

^{2}**2. How much time would it take to go from 10 m/s to 35 m/s in 50 meters?**

**3. How much did you accelerate when starting from rest and traveling 230 meters in 15 seconds?**

**4. How far would you have traveled after starting from 2 m/s and speeding up to 12 m/s at 3 m/s**^{2}?

^{2}?

**Links**

**Continue to Part 3: Acceleration Due to Gravity**- Back to the
**Stickman Physics Home Page** - For video tutorials and other physics resources check out
**HoldensClass.com** - Find many of your animation resources in one place at the
**StickMan Physics Gallery** **Equation Sheet**