# Acceleration vs. Velocity Equations

## Useful equations related to acceleration, average velocity, final velocity and distance traveled.

### Average Velocity

*v _{a} = (v_{1} + v_{0}) / 2 (1)*

*where *

*v _{a} = average velocity (m/s)*

*v _{0} = initial velocity (m/s)*

*v _{1} = final velocity (m/s)*

### Final Velocity

*v _{1} = v_{0} + a t (2)*

*where *

*a = acceleration (m/s ^{2})*

*t = time taken (s)*

### Distance Traveled

*s = (v _{0} + *

*v*

_{1})*t / 2 (3)*

*where *

*s = distance traveled (m)*

Alternative:

*s = v _{0} t + 1/2 a t^{2} (3b)*

### Acceleration

*a = (v _{1} - *

*v*

_{0}) /*t (4)*

Alternative:

*a = (v _{1}^{2} - *

*v*

_{0}^{2}) /*(2 s) (4b)*

### Example - Accelerating Motorcycle

A motorcycle starts with an initial velocity *0 km/h (0 m/s)* and accelerates to *120 km/h (33.3 m/s)* in *5 s*.

The average velocity can be calculated with eq. *(1)* to

*v _{a} = ((33.3 m/s) - (0 m/s)) / 2 *

* = 16.7 m/s*

The distance traveled can be calculated with eq. *(3)* to

*s = ( (0 m/s) + *

*(33.3 m/s)*) (5 s)*/ 2*

* = 83.3 m *

The acceleration can be calculated with eq. *(4)* to

*a = ( (33.3 m/s) - *

*) /**(0 m/s)**(5 s)*

* = 6.7 m/s ^{2}*

- compare with acceleration of gravity