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, vi represents initial velocity and vf represents the final velocity.

Acceleration Equation Variables

Name Variable Unit Unit Abbreviation
Initial Velocity or Initial Speed vi meters per second m/s
Final Velocity or Final Speed vf meters per second m/s
Time t seconds s
Acceleration a meters per second squared m/s2
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.

acceleration equation

With change in velocity expanded out below:

acceleration equation

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

vf = vi + at

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

x = vit + ½ at2

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

vf2=vi2 + 2ax

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

x = ((vi + vf)/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.

picking the right acceleration equation

Example question as you walk through the steps.  How fast was Chancellor running after starting from rest and accelerating at 4.5 m/s2 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: vf = ?)
  • Step three: pick out the variables given in the equation. (example: vi = 0 m/s, a= 4.5 m/s2, 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: vf = vi + 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 (vf = vi + 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 vf2 = vi2 + 2ax. to solve for vf you need to make vf2 become vf 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/s2 for three seconds?

Example 1 Acceleration

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

Example 2 Acceleration

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

Example 3 Acceleration

4.  How far would you have traveled after starting from 2 m/s and speeding up to 12 m/s at 3 m/s2?

Example 4 Acceleration

Accelerated Motion Quiz

Do you know your variables and how to pick either the constant motion equation or one of the acceleration ones?

picking the right acceleration equation

Find out by taking this quiz

1 / 10

A change in velocity over time is ______________.

2 / 10

A change in displacement over time is ______________.

3 / 10

Which variable is bold in the following question:

How fast was Sam traveling if he is traveling at 16 m/s after accelerating at 2 m/s2 for 25 meters?

A) vi

B) vf

C) a

D) t

E) x

F) v

4 / 10

Which variable is bold in the following question:

How fast was Sam traveling if he is traveling at 16 m/s after accelerating at 2 m/s2 for 25 meters?

A) vi

B) vf

C) a

D) t

E) x

F) v

5 / 10

Which variable is bold in the following question:

How fast was Sam traveling if he is traveling at 16 m/s after accelerating at 2 m/s2 for 25 meters?

A) vi

B) vf

C) a

D) t

E) x

F) v

6 / 10

Pick the right equation:

How far did Tony travel when he constantly accelerated from 5 to 15 m/s in 5 seconds?

Accleleration and constant velocity equations

7 / 10

Solve the problem using the right equation:

How fast was Sam traveling if he is traveling at 16 m/s after accelerating at 2 m/s2 for 25 meters?

Accleleration and constant velocity equations

8 / 10

Pick the right equation and solve the problem:

What is the acceleration of a person that accelerates from 10 m/s to 30 m/s in 5 seconds?

Accleleration and constant velocity equations

9 / 10

Pick the right equation and solve the problem:

How far did Tony travel when he constantly accelerated from 5 to 15 m/s in 5 seconds?

Accleleration and constant velocity equations

10 / 10

Pick the right equation and solve the problem:

A duck flew 500 meters in 40 seconds.  How fast was the duck flying?

Accleleration and constant velocity equations

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