December 24, 2025
Struggling to tackle those constant acceleration problems in A-Level Mechanics? You’re not alone. The SUVAT equations are a fundamental toolkit for physics, but knowing when and how to use them is the key to exam success. This guide will break down everything you need to know—from understanding the variables to solving complex problems step-by-step—helping you move from confusion to confidence.
SUVAT equations are a set of four formulas that describe the motion of an object moving in a straight line with constant (uniform) acceleration. The name "SUVAT" comes from the five key variables involved. Mastering these is essential for the "Mechanics and Materials" section of your AQA (and other) A-Level Physics syllabus.
Before using the equations, you must be crystal clear on what each symbol represents. Remember, displacement, velocity, and acceleration are all vector quantities. This means direction matters, and you must define a positive direction (e.g., upwards or to the right) at the start of every problem.
|
Symbol |
Quantity |
SI Unit |
Key Notes & Tips |
|
s |
Displacement |
Metres (m) |
The straight-line change in position from start to finish. Not the same as total distance travelled. |
|
u |
Initial Velocity |
Metres per second (m/s or m s⁻¹) |
The object's velocity at the start of your time period. "Starts from rest" means u = 0. |
|
v |
Final Velocity |
Metres per second (m/s or m s⁻¹) |
The object's velocity at the end of your time period. |
|
a |
Constant Acceleration |
Metres per second squared (m/s² or m s⁻²) |
Must be constant. For free fall near Earth, a = g = ±9.81 m/s². The sign depends on your chosen direction. |
|
t |
Time Interval |
Seconds (s) |
The period over which the motion occurs. |
You do not need to memorise all of these for some exam boards (like AQA, where they are provided), but knowing how they link the variables is crucial. Here they are:
Memory Tip: The first equation (v = u + at) is the most intuitive (final speed equals starting speed plus change). The third is less common. Focus on identifying which variables you have and which one you need to find.
This systematic approach will work for every SUVAT problem you encounter.
Write down the five SUVAT letters: s, u, v, a, t.
Extract their values from the question. Convert all units to SI units (metres, seconds).
Identify the unknown you need to find.
CRUCIAL: Define a positive direction (e.g., "up is positive"). Apply + or – signs to all vector quantities (s, u, v, a) based on this direction.
Step 2: Choose the Right Equation
Look at your list. Which equation contains the three known variables and the one unknown you want?
The equation you choose must have the unknown in it and must not include the variable you don't know or care about.
Step 3: Substitute & Solve
Substitute your values (with their signs!) into the chosen equation.
Rearrange the equation algebraically to solve for the unknown.
Finally, interpret your answer, including its sign (e.g., a negative velocity means motion in the negative direction).
Let's apply the 3-step method.
Example 1: Basic Application
*A car accelerates from rest at 3 m/s² for 5 seconds. What is its final velocity and how far does it travel?*
List: Positive direction = direction of motion.
s = ? (what we want, part 2)
u = 0 m/s ("from rest")
v = ? (what we want, part 1)
a = +3 m/s²
t = 5 s
Choose:
For *v*: Use v = u + at (we know u, a, t).
For *s*: Use s = ut + ½at² (we know u, a, t and just found v, but we don't need v for this equation).
Solve:
v = 0 + (3)(5) = 15 m/s
s = (0)(5) + ½(3)(5)² = 0 + ½(3)(25) = 37.5 m
Example 2: Involving Direction (Projectile)
*A ball is thrown vertically upwards at 12 m/s. What is the maximum height it reaches? (Take g = 9.81 m/s²)*.
List: Positive direction = upwards.
s = ? (maximum height)
u = +12 m/s (upwards)
v = 0 m/s (at the highest point, it momentarily stops)
a = -9.81 m/s² (acceleration due to gravity acts downwards, opposite to our positive direction)
t = ? (not needed)
Choose: We know u, v, a and want s. We don't know or need t. The perfect equation is v² = u² + 2as.
Solve:
(0)² = (12)² + 2(-9.81)s
0 = 144 - 19.62s
19.62s = 144
s ≈ 7.34 m
|
Pitfall |
Why It's Wrong |
How to Avoid It |
|
Mixing up 's' for displacement with distance. |
A 10m journey there and back gives a distance of 20m but a displacement of 0m. |
Always ask: "What is the straight-line change in position from start to finish?" |
|
Ignoring vector signs (+, -). |
This is the #1 cause of errors. Using u=12 and a=9.81 for the upward throw gives a nonsense answer. |
Step 1 is always DEFINE your positive direction. Stick to it rigidly for all vectors. |
|
Using SUVAT for non-constant acceleration. |
SUVAT only works if 'a' is constant. Motion with changing forces (e.g., air resistance) isn't SUVAT. |
Check the question: does it say "uniform acceleration" or "constant acceleration"? If not, SUVAT may not apply. |
|
Not converting units. |
Using km/h or minutes directly will give an incorrect answer. |
Convert everything to metres and seconds before you start Step 2. |
The SUVAT equations are a powerful, predictable part of your physics exam. Success comes from:
Understanding the variables as vectors.
Applying the 3-step strategy religiously for every problem.
Practising relentlessly.
The best way to prepare? Use the past papers and worksheets available right here on Merit Study Resources to find as many SUVAT problems as you can. Start with the basics, then challenge yourself with multi-stage problems. With consistent practice, you’ll be able to look at any kinematics question and know exactly which equation is your key to unlocking the marks.
Ready to test your skills? Search our database for past papers on "Mechanics" or "Equations of Motion" and put your knowledge into practice!
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