Lesson focus: Constant-acceleration equations connect initial velocityThe velocity at the start of a journey or time period (u)., final velocityThe velocity at the end of a journey or time period (v)., acceleration, time and displacement when their conditions are satisfied.
Select and use a = (v − u)/t and v² = u² + 2as for one-dimensional constant-acceleration motion.
Build on earlier learning
Velocity and acceleration graphsThe previous lesson derived acceleration and displacement from velocity–time graphs. This lesson expresses the same constant-acceleration model algebraically.
You will be successful when you can…
- Define u, v, a, s and t.
- Select an equation from known values.
- Use consistent signs and units.
- Check constant-acceleration assumptions.
Words that carry the science
- SUVAT
- A label for displacement s, initial velocity u, final velocity v, acceleration a and time t.
- initial velocity
- Velocity u at the start of the chosen interval.
- final velocity
- Velocity v at the end of the chosen interval.
- uniform acceleration
- Constant acceleration throughout the interval.
- kinematic equation
- An equation relating motion quantities without directly naming the forces.
- model assumption
- A condition accepted so a mathematical representation can be used.
Choose quantities before choosing an equation
01Choose quantities before choosing an equation
Define a positive direction, list known values with units and identify the unknown. The symbols are s displacement, u initial velocityThe velocity at the start of a journey or time period (u)., v final velocityThe velocity at the end of a journey or time period (v)., a acceleration and t time.
Use a = (v − u)/t when time is involved. Use v² = u² + 2as when time is absent.
02Signs carry direction information
A velocity or acceleration opposite the positive direction is negative. Displacement also carries a sign; distance does not.
For braking with forward positive, u is positive and a is negative. The term 2as then reduces v² as expected.
03SUVAT is a constant-acceleration model
These equations apply only when acceleration is constant over the chosen interval. They are not valid across changing drag, multiple stages or curved two-dimensional motion without careful separation.
A calculator result does not repair an invalid model. Check whether forces and acceleration are reasonably constant.
SUVAT with a moving car
When acceleration is constant, five quantities are linked: displacement s, initial velocity u, final velocity v, acceleration a and time t. Set u, a and t, watch the car, and check that the equations agree. The animation runs at double speed.
Controls
Find braking displacement
A car slows from 20 m s⁻¹ to rest at constant acceleration −5.0 m s⁻².
- Choose forward as positive: u = 20, v = 0, a = −5.0.
- Use v² = u² + 2as because time is not given.
- 0² = 20² + 2(−5.0)s.
- Rearrange: s = 400 ÷ 10 = 40 m.
How to make the reasoning visible: The braking displacement is 40 m under the constant-deceleration model.
Select the valid relationship
Identify the missing variable and solve only where constant acceleration is stated.
| Known values | Unknown | Equation | Result |
|---|---|---|---|
| u=0, v=16, t=8 s | a | a=(v−u)/t | 2 m s⁻² |
| u=10, a=3, s=24 m | v | v²=u²+2as | 15.6 m s⁻¹ |
| u=25, v=0, a=−6.25 | s | v²=u²+2as | 50 m |
| changing drag throughout fall | v | neither directly | acceleration not constant |
Why is the final row unsuitable?
Why take the positive square root in row two?
Check your understanding
Answer from memory, then check against the suggested answer.
What does s represent?
State the no-time SUVAT equation.
What condition must hold?
A ball’s acceleration changes because air resistance grows. Can one SUVAT calculation model the whole fall?
How does v² = u² + 2as agree with a velocity–time graph?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
A cyclist accelerates uniformly from 6.0 m/s at 1.4 m/s² over a distance of 35 m.
Calculate the final speed. Use v² = u² + 2as and show your working.
(5)Total for this question: 5 marks
Command word: For calculateA command word: work out a number answer, showing your working and the unit., select the equation by the variables present and state the constant-acceleration assumption.