SUVAT Equations of Motion

Apply constant acceleration kinematic equations in A-Level Mechanics: v = u + at, s = ut + ½at², v² = u² + 2as.

Learning Objectives

Define the SUVAT variables: Displacement (s), Initial velocity (u), Final velocity (v), Acceleration (a), Time (t)
Select the appropriate SUVAT formula based on given and required variables
Solve vertical motion problems under gravity g = 9.8 m/s²
Interpret displacement-time and velocity-time graphs

Concept Explanation

SUVAT equations form the foundation of classical kinematics in A-Level Mechanics. They describe the motion of an object moving in a straight line with CONSTANT acceleration.

SUVAT Letters: s = displacement (m), u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (s).

Rule 1: SUVAT equations only apply when acceleration is constant.

Rule 2: Direction matters! Assign a positive direction (e.g. upwards = positive). Gravity acts downwards, so a = -9.8 m/s² when moving upwards.

At maximum height of vertical motion, final velocity v = 0 m/s.

Key Mathematical Formulas

v = u + at

s = \frac{u + v}{2} t

s = ut + \frac{1}{2}at^2

v^2 = u^2 + 2as

s = vt - \frac{1}{2}at^2

Worked Example

Step-by-Step Solution

Interactive Walkthrough

Problem Statement:

A ball is thrown vertically upwards from ground level with an initial speed of 14 m/s. Calculate the maximum height reached. (Take g = 9.8 m/s²)

u = 14\text{ m/s}, \quad v = 0\text{ m/s (at peak)}, \quad a = -9.8\text{ m/s}^2, \quad s = ?

Step 1: List known SUVAT variables and select equation

We know u = 14, v = 0, a = -9.8, and need s. The equation linking u, v, a, s without time t is v² = u² + 2as.

v^2 = u^2 + 2as

Final Answer:

s = 10\text{ metres}

Try It Yourself

A car accelerates uniformly from rest (u = 0) to 20 m/s in 5 seconds. What distance s did the car travel?

s = \frac{u + v}{2} t

Common Student Mistakes

❌ Common Pitfall: Mixing up scalar distance with vector displacement

✅ Correction: Displacement can be negative if the object returns below its starting position.

❌ Common Pitfall: Forgetting gravity is negative when resolving upwards

✅ Correction: If upward is positive, downward acceleration due to gravity is a = -9.8 m/s².

UK Exam Advice & Tips

Check your UK exam board formula sheet: Edexcel uses g = 9.8 m/s², while OCR/AQA may specify g = 9.81 m/s².

Lesson FAQ

Can I use SUVAT when acceleration changes over time?

No. For variable acceleration (e.g. a = 3t²), you must use calculus: differentiate velocity to get acceleration, or integrate acceleration to get velocity.

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