Section 1 of 5The Equation of Motion
This equation applies only when acceleration is uniform, which means it is constant.
Equation
- v² = u² + 2as, which links initial velocity, final velocity, acceleration and distance.
Symbol u
- The initial velocity in m/s, which is zero if the object starts from rest.
Symbol v
- The final velocity in m/s, found at the end of the distance considered.
Symbol a
- The uniform acceleration in m/s², which must be constant over the distance.
Symbol s
- The distance moved in metres during the acceleration.
Section 2 of 5Solving for an Unknown
Writing down the known values first makes the choice of equation clear.
1
List the known quantities u, v, a and s, and label the one that must be found.
2
Choose the equation v² = u² + 2as, because time is not given in the question.
3
Rearrange the equation to make the unknown the subject, doing the same to both sides.
4
Substitute the values, using squares carefully, and calculate the answer with units.
Section 3 of 5Common Situations
Common Situations
Starting from rest
- When the object starts from rest, u is zero, so v² equals 2as.
Braking
- When an object stops, v is zero and the acceleration is negative.
Finding acceleration
- Rearranging gives a = (v² − u²) ÷ 2s, which is useful when distance is known.
Units check
- Using m/s and m gives m²/s² in the equation, which must balance on both sides.
Section 4 of 5Worked Example
Question
- A train accelerates uniformly from rest to a speed of 24 m/s with an acceleration of 3 m/s².
- Calculate the distance travelled during this acceleration.
- Known valuesu = 0 m/s, v = 24 m/s, a = 3 m/s², s = ?
- Equationv² = u² + 2as.
- Rearranges = (v² − u²) ÷ (2a).
- s = (24² − 0²) ÷ (2 × 3) = 576 ÷ 6 = 96 m.
Answer The train travels 96 m during the acceleration.
Section 5 of 5Exam Checklist & Tips
1.1.7 – Key Points for the Exam
- Uniform acceleration Constant acceleration, where velocity changes by the same amount each second.
- Equation of motion An equation that links velocity, acceleration and distance for uniform acceleration.
- Initial velocity The velocity of an object at the start of the motion, written as u.
- Rearranging Changing the subject of an equation by performing the same operation on both sides.
Common Mistakes
- Writing the equation as v = u + 2as, which is not correct; the velocities must be squared.
- Forgetting to square the velocities before subtracting when rearranging the equation.
- Using this equation when the acceleration is not uniform, which gives a wrong answer.
- Leaving the answer for distance negative, or failing to check that the unit is metres.