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# Acceleration vs. Velocity Equations

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

### Average Velocity

va = (v1 + v0) / 2                    (1)

where

va = average velocity (m/s)

v0 = initial velocity (m/s)

v1 = final velocity (m/s)

### Final Velocity

v1 = v0 + a t                   (2)

where

a = acceleration (m/s2)

t = time taken (s)

### Distance Traveled

s = (v0 + v1) t / 2                   (3)

where

s = distance traveled (m)

Alternative:

s = v0 t + 1/2 a t2                 (3b)

### Acceleration

a = (v1 - v0) / t                    (4)

Alternative:

a = (v12 - v02) / (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

va = ((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

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

a = ( (33.3 m/s) -  (0 m/s)) / (5 s)

= 6.7 m/s2

## Related Topics

• Dynamics - Motion - velocity and acceleration, forces and torque.

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