Acceleration vs. Velocity Equations

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

Average Velocity

Formula: va = (v1 + v0) / 2

where:

va = average velocity (m/s)
v0 = initial velocity (m/s)
v1 = final velocity (m/s)

Calculator

Inputs

Initial Velocity (v0) (m/s)

Final Velocity (v1) (m/s)

Results

Average Velocity-- m/s

Final Velocity

Formula: v1 = v0 + a·t

where:

a = acceleration (m/s²)
t = time taken (s)

Calculator

Inputs

Initial Velocity (v0) (m/s)

Acceleration (a) (m/s²)

Time (t) (s)

Results

Final Velocity-- m/s

Distance Traveled

Formula: s = (v0 + v1)·t / 2

Alternative: s = v0·t + ½·a·t²

where:

s = distance traveled (m)
v0 = initial velocity (m/s)
v1 = final velocity (m/s)
a = acceleration (m/s²)
t = time taken (s)

Calculator

Inputs

Initial Velocity (v0) (m/s)

Final Velocity (v1) (m/s)

Time (t) (s)

Results

Distance Traveled-- m

Acceleration

Formula: a = (v1 - v0) / t

Alternative: a = (v1² - v0²) / (2·s)

where:

a = acceleration (m/s²)
v0 = initial velocity (m/s)
v1 = final velocity (m/s)
t = time taken (s)
s = distance traveled (m)

Calculator

Inputs

Initial Velocity (v0) (m/s)

Final Velocity (v1) (m/s)

Time (t) (s)

Results

Acceleration-- m/s²

Example - Accelerating Motorcycle

A motorcycle starts with an initial velocity of 0 km/h (0 m/s) and accelerates to 120 km/h (33.3 m/s) in 5 seconds.

Average Velocity:

va = (33.3 m/s + 0 m/s) / 2 = 16.7 m/s

Distance Traveled:

s = (0 m/s + 33.3 m/s) × 5 s / 2 = 83.3 m

Acceleration:

a = (33.3 m/s - 0 m/s) / 5 s = 6.7 m/s²