# Acceleration vs. Velocity Equations

### 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

## Related Topics

### • Dynamics

Motion - velocity and acceleration, forces and torque.

## Related Documents

### Acceleration

Change in velocity vs. time used.

### Acceleration Units Converter

Converting between units of acceleration.

### Average Velocity

Distance traveled vs. time used.

### Car Acceleration

Car acceleration calculator.

### Velocity Units - Online Converter

Convert between common velocity and speed units.

### Velocity Units Converter

Convert between speed and velocity units like *m/s, km/h, knots, mph and ft/s*.