# Motion with constant acceleration review

Review the key concepts, equations, and skills for motion with constant acceleration, including how to choose the best kinematic formula for a problem.

## Key terms

Term | Meaning |
---|---|

Kinematic variable | Variable that describes the motion of an object over time. Includes displacement $\Delta x$ , time interval $t$, initial velocity $v_0$, final velocity $v$, and acceleration $a$. |

Kinematic formula | Formula that describes the relationships between kinematic variables when acceleration is constant. |

## Equations

- $v=v_0 + at$
- $x = x_0 + v_0t + \dfrac{1}{2}at^2$
- $v^2 = v_0^2 + 2a(x-x_0)$
- $x - x_0 = \dfrac{1}{2}(v_0 + v)t$

**Symbols**

- $x_0$ is
- $x$ is the
- $t$ is the
- $v_0$ is initial velocity
- $v$ is final velocity
- $a$ is acceleration

**Assumptions**

- Acceleration is constant over the time interval

## Using the kinematic formulas

### Choosing the best kinematic formula

To choose the kinematic formula that's right for your problem, figure out

**which variable you are not given and not asked to find.**For example, we could use $v = v_0 + at$ to solve for the variables $v$, $v_0$, $a$, or $t$ if we knew the values of the other three variables. Note that each kinematic formula is missing one of the five kinematic variables.

### Finding the known variables

Sometimes a known variable will not be explicitly given in a problem, but rather implied with

**codewords**. For instance, "starts from rest" means $v_0=0$, "dropped" often means $v_0=0$, and "comes to a stop" means $v=0$.Also, the magnitude of the acceleration due to gravity on all objects in free fall on Earth is usually assumed to be $g=9.8\dfrac{\text{m}}{\text{s}^2}$, so this acceleration will usually not be given explicitly.

## Common mistakes and misconceptions

**People forget that some of the kinematic variables are vectors and can have negative signs.**For example, if upward is assumed to be positive, then the acceleration due to gravity must be negative: $a_g=-9.81\dfrac{\text{m}}{\text{s}^2}$. A missing negative sign is a very common mistake, so don't forget to check which direction is defined as positive!**People forget that the kinematic variables we plug into a kinematic formula must be consistent with that time interval.**In other words, the initial velocity $v_0$ has to be the velocity of the object at the initial position and start of the time interval $t$. Similarly, the final velocity $v$ must be the velocity at the final position and end of the time interval $t$.**The second kinematic equation, $x=x_0+ v_0 t+\dfrac{1}{2}at^2$, might require using the**.

## Learn more

For deeper explanations, see our videos choosing kinematic equations and a worked example with kinematic equations.

To check your understanding and work toward mastering these concepts, check out our exercises choosing the best kinematic equation and solving problems with kinematic equations.