# Acceleration

## Change in velocity and time used

Acceleration is the ratio *change in velocity* to *time used* and can be expressed as

a = dv / dt

= (v_{1}- v_{0}) / (t_{1}- t_{0}) (1)

where

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

dv = change in velocity (m/s, ft/s)

v_{1}= final speed (m/s, ft/s)

v_{0}= initial speed (m/s, ft/s)

dt = time taken (s)

t_{1}= final time (s)

t_{0}= initial time (s)

### Example - Motorcycle Acceleration

If a motorcycle accelerates from *0 km/h* to *100 km/h* in *3 seconds*, the acceleration can be calculated as

a = ((100 km/h) - (0 km/h)) (1000 m/km) / (3600 s/h)) / (3 s)

= 9.26 (m/s^{2})

or close to acceleration of gravity* 1 g = 9.81 (m/s ^{2})*.

The time from *0 - 100 km/h* for an acceleration equal to gravity can be calculated by modifying the equation above to

*(9.81 m/s ^{2}) = ((100 km/h) - (0 km/h)) (1000 m/km) / (3600 s/h)) / dt*

*or *

*dt = ((100 km/h) - (0 km/h)) (1000 m/km) / (3600 s/h)) / (9.81 m/s^{2})*

* = 2.83 s*

### Acceleration Calculator

The calculator below can be used to calculate acceleration:

v_{0}-initial velocity

v_{1}-final velocity

km/h m/s mph ft/s

time taken (s)