**LIST OF KINEMATIC EQUATIONS FOR CONSTANT ACCELERATION**

Kinematic equations for constant acceleration are composed of four equations relating position, velocity, acceleration, and time, when the acceleration a is constant. Kinematic equations are not valid unless acceleration (a) is a constant. The four kinematic equations are listed below.

x=x_{0}+v_{0}t+1/2at^{2 }(x related to a and t)

x= x_{0} + 1/2(v+v_{0})t (x related to v and t)

v=v_{0}+at (v related to a and t)

v^{2}=v_{0}^{2}+2a(x-x_{0}) (v related to a and x)

In many cases initial position (x_{0}) is set to 0 to simplfy the equations. These equations are used to calculate the parameters of an object’s motion.

List of parameters used In equations are:

x_{0} |
Initial position |

x | Position at time t |

x-x_{0} |
Displacement |

v_{0} |
Initial velocity |

v | Velocity at time t |

a | Acceleration |

t | Elapsed time. |

## Kinematic Equation Example

A car starts from standstill and accelerates at a constant acceleration of 5 m/s^{2} during 600 m distance. How fast is the car going at the end of 600 m?

**Solution: **

v^{2}=v_{0}^{2}+2a(x-x_{0})

v^{2}=0 +2(5 m/s^{2})(600 m) =6000 m^{2}/s^{2}

v = (6000 m^{2}/s^{2} )^{0.5 } = 77.5 m/s

## Additional Resources

## Reference

- Giancoli, Douglas C. Physics: Principles with Applications (7th Edition) – Standalone book. Pearson, 2016.