Acceleration vs. Velocity Equations

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

v_a = (v₁ + v₀) / 2 (1)

where

v_a = average velocity (m/s)

v₀ = initial velocity (m/s)

v₁ = final velocity (m/s)

v₁ = v₀ + a t (2)

where

a = acceleration (m/s²)

t = time taken (s)

s = (v₀ + v₁) t / 2 (3)

where

s = distance traveled (m)

Alternative:

s = v₀ t + 1/2 a t² (3b)

a = (v₁ - v₀) / t (4)

Alternative:

a = (v₁²- v₀²) / (2 s) (4b)

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