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Acceleration vs. Velocity Equations

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

Average Velocity

v a = (v1 + v0 ) / 2                    (1)


v a = average velocity (m/s)

v0 = initial velocity (m/s)

v1 = final velocity (m/s)

Final Velocity

v1 = v0 + a t                   (2)


a = acceleration (m/s2)

t = time taken (s)

Distance Traveled

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


s = distance traveled (m)


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


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


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

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/s2

Related Topics

  • Dynamics

    Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.

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