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# 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

= (v1 - v0) / (t1 - t0)      (1)

where

a = acceleration (m/s2, ft/s2)

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

v1 = final speed (m/s, ft/s)

v0 = initial speed (m/s, ft/s)

dt = time taken (s)

t1 = final time (s)

t0 = 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/s2)

or close to acceleration of gravity 1 g = 9.81 (m/s2)

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/s2) = ((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/s2)

= 2.83 s

### Acceleration Calculator

The calculator below can be used to calculate acceleration:

v0 - initial velocity

v1 - final velocity

km/h m/s mph ft/s

time taken (s)

## Related Topics

• Dynamics - Motion - velocity and acceleration, forces and torques

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