KinexiaLEARN PHYSICS

SUVAT Velocity — Rocket Second-Stage Burn (Worked Example)

Medium
Problem

A sounding rocket is already travelling at 200 m/s when its second stage ignites, accelerating it uniformly at 12 m/s² for 45 s. What is its velocity at burnout?

Given

  • u = 200 m/s

  • a = 12 m/s²

  • t = 45 s

Find

The burnout velocity v.

Principle

Each second of burn adds a fixed velocity increment (a × 1 s). Over the whole burn, v = u + at gives the final velocity directly.

Formula

Solution

  1. Write the equation: v=u+atv = u + at

  2. Substitute: v=200+(12)(45)v = 200 + (12)(45)

  3. Velocity gained: 12×45=540 m/s12 \times 45 = 540\ \mathrm{m/s}

  4. Add: v=200+540=740 m/sv = 200 + 540 = 740\ \mathrm{m/s}

740 m/s

Unit check

m/s² × s = m/s, added to m/s. Units are consistent throughout.

What this means physically

740 m/s is more than twice the speed of sound. At this speed aerodynamic heating becomes a serious design concern — which is why the second stage fires high in the atmosphere where the air is thin.

Common mistake

Using the burn time in minutes instead of seconds. SUVAT equations require SI-consistent units: convert every time to seconds before substituting.