Menu

SUVAT Equations Explained: Simple Breakdown with Examples

SUVAT Equations Explained: Simple Breakdown with Examples

The SUVAT equations are a set of five kinematic equations used in physics to describe motion under constant acceleration. They are particularly useful for solving problems involving velocity, acceleration, displacement, and time. 

The term SUVAT comes from the five key variables:

  • s – Displacement (distance moved in a particular direction)
  • u – Initial velocity (starting speed)
  • v – Final velocity (speed at the end)
  • a – Acceleration (rate of change of velocity)
  • t – Time (duration of motion)

1. The Five SUVAT Equations

Each equation is used depending on the known and unknown variables in a problem. How to Improve Your Child’s Reading Comprehension

01. v=u+atv = u + at

  • No ss (displacement)
  • Use when you need to find final velocity but don’t have displacement.

02. s=ut+12at2s = ut + \frac{1}{2} at^2

  • No vv (final velocity)
  • Use when you need to find displacement but don’t have final velocity.

03. v2=u2+2asv^2 = u^2 + 2as

  • No tt (time)
  • Use when you need to find final velocity or acceleration but don’t have time.

04. s=(u+v)2ts = \frac{(u + v)}{2} t

  • No aa (acceleration)
  • Use when you need to find displacement but don’t have acceleration.

05. s=vt−12at2s = vt – \frac{1}{2} at^2

  • No uu (initial velocity)
  • Use when you need to find displacement but don’t have initial velocity.

2. Example Problems

Example 1: Finding Final Velocity

Question: A car starts at 5 m/s and accelerates at 3 m/s² for 4 seconds. What is its final velocity? Become an Education Franchise Partner with LTSchool

Given:

  • u=5u = 5 m/s
  • a=3a = 3 m/s²
  • t=4t = 4 s
  • v=?v = ?

Using: v=u+atv = u + at

v=5+(3×4)v = 5 + (3 \times 4) v=5+12=17 m/sv = 5 + 12 = 17 \text{ m/s}

Answer: The final velocity is 17 m/s.

Example 2: Finding Displacement

Question: A bike starts from rest and accelerates at 2 m/s² for 6 seconds. How far does it travel? Let’s connect for Online tutoring UK

Given:

  • u=0u = 0 m/s
  • a=2a = 2 m/s²
  • t=6t = 6 s
  • s=?s = ?

Using: s=ut+12at2s = ut + \frac{1}{2} at^2

s=(0×6)+12(2×62)s = (0 \times 6) + \frac{1}{2} (2 \times 6^2) s=0+12(2×36)s = 0 + \frac{1}{2} (2 \times 36) s=0+12(72)s = 0 + \frac{1}{2} (72) s=36 ms = 36 \text{ m}

Answer: The bike travels 36 meters.

Example 3: Finding Acceleration

Question: A train slows down from 30 m/s to 10 m/s over a distance of 160 meters. What is its acceleration?

Given:

  • u=30u = 30 m/s
  • v=10v = 10 m/s
  • s=160s = 160 m
  • a=?a = ?

Using: v2=u2+2asv^2 = u^2 + 2as

102=302+2a(160)10^2 = 30^2 + 2a(160) 100=900+320a100 = 900 + 320a 320a=100−900320a = 100 – 900 320a=−800320a = -800 a=−2.5 m/s2a = -2.5 \text{ m/s}^2

Answer: The acceleration is -2.5 m/s² (negative because the train is slowing down).

3. Key Exam Tips

  • Identify the known and unknown values before selecting an equation.
  • Check which variable is missing—this helps in choosing the correct SUVAT equation.
  • Use negative acceleration when an object is slowing down.
  • Ensure all units are consistent (meters, seconds, m/s²).
  • Double-check calculations to avoid simple mistakes.

Final Thoughts

Understanding and practicing the five SUVAT equations will help you tackle physics problems efficiently. Keep practicing different question types, and soon, these equations will become second nature! Learn to code, read the Future of coding