Calculating Average Acceleration of a Roller Coaster

A roller coaster accelerates from **4 m/s to 22 m/s in 3 seconds**. Find the average acceleration.

Formula

Average acceleration (\(a_{avg}\)) = \(\frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}\)

Given

• Initial velocity (\(v_i\)) = 4 m/s
• Final velocity (\(v_f\)) = 22 m/s
• Time interval (\(t\)) = 3 s

Calculation

\(a_{avg} = \frac{22 \, \text{m/s} - 4 \, \text{m/s}}{3 \, \text{s}} = \frac{18 \, \text{m/s}}{3 \, \text{s}} = \mathbf{6 \, \text{m/s}^2}\)

Interpretation

• The coaster's velocity increases by **6 m/s every second** on average.
• This is **~0.61 g** (where 1 g = 9.81 m/s²) — a strong but comfortable acceleration for a launched coaster.
• Real coasters have **variable acceleration** (peak > average during launch; negative during brakes/hills).

Average acceleration is a useful simplification for overall performance comparison.