Kinematics is a large topic in the Mechanics paper, and it mixes two toolkits: the constant acceleration equations and calculus. The reports show that most students handle the routine questions well. The marks go missing when the motion changes, when two particles are involved, and when calculus is needed. This guide collects what Cambridge examiners say students get wrong, based on recent reports.
Summarised in our own words from a reading of the examiner reports.
Mistakes that cost marks
- Using the constant acceleration equations when acceleration is not constant. When velocity or acceleration is given as a function of time, calculus must be used. This is a key message in many sessions.
- The constant of integration. The most common error in one question was to set up an equation from a velocity expression that had no constant term, because students assumed the constant would be zero. Others omitted the constant from the displacement expression, or assumed C = 0 without checking the initial conditions.
- Distance and displacement. Integrating over the whole interval gives displacement. When the velocity changes sign, split the interval. One reported wrong answer was 4 m, from using limits of 0 and 4 instead of integrating over three separate intervals. Limits of 0 and 2 gave zero in another question. Students also assumed the value of the integrand was 0 when t = 0, and obtained the same incorrect answer.
- Wrong assumptions about the graph. Students who assumed that a velocity-time graph was made of straight lines found areas using triangles and trapezia, with no integration. When drawing graphs, students often drew curves where straight lines were needed, or did not annotate the axes correctly. For constant velocity sections, a horizontal line is expected, and only a minority drew the right shape.
- Signs and gravity. Reports record 5 = u + (−10) × 2, using a = −g with u = 0 when v = 0 was meant, or using a = g with u = 30. Finding the time to reach the highest point and doubling it was another common error when the start and end heights differed.
- Velocity and speed. In one question students found −29.4 m/s correctly and did not state the speed 29.4 m/s, which the question asked for.
- Two particles. Common errors included using the same expression for the time in both equations, using T + 1 instead of T − 1, finding the time for only one particle, forgetting that the second particle starts later, and treating the initial velocity of one particle as that of the other.
- Constant acceleration equations used wrongly. One report describes students who put v = 10 and g = 10 into v² = u² + 2as, which gave the correct answer from clearly incorrect working. Another describes students who assumed constant speed when calculating a final speed.
- Misreading the question. Students gave a total time that was not the one asked for, such as the time with the string slack, or the time of upward motion only. In a question about a car and a trailer, some included only the car.
- Algebra. Errors in factorising a quadratic, using the quadratic formula, and working with fractional powers.
- Accuracy and form. Answers expressed in decimals when fractions were better, or wrongly stated to 3 significant figures.
What examiners advise
- Annotate diagrams and graphs clearly: label axes, times, velocities and which object is which.
- Look at the form of the information in the question. A function of t means calculus.
- Split the interval when the velocity changes sign and you need a distance.
- Define your direction of positive and use it consistently for velocity, acceleration and gravity.
- Show your method when the answer is given. Do not use v = 10 and g = 10 together to force a result.
- Divide total distance by total time for average speed, as the reports note this is accurate and efficient.
Habits that help
- Write what you are given as u, v, a, s and t in a list before choosing an equation.
- For two particles, write each particle's displacement formula on separate lines, with its own time.
- Check that the sign of your answer matches the direction of motion.
Questions students ask
When can I use the constant acceleration (suvat) equations?
Only when acceleration is constant. When velocity or acceleration is given as a function of time, calculus must be used. Examiners repeat this in many sessions.
What is the difference between distance and displacement in kinematics?
Integrating over the whole interval gives displacement. When the velocity changes sign, split the interval to find distance. One reported wrong answer was 4 m, from using limits of 0 and 4 instead of integrating over each part separately.
Do I need a constant of integration when I integrate acceleration to get velocity?
Yes. A common error was setting up an equation from a velocity expression with no constant because students assumed it would be zero. Use the given information to find it.
How do I handle gravity and signs?
Define the positive direction and use it consistently for velocity, acceleration and gravity. Reports record 5 = u + (−10) × 2, a = −g with u = 0 when v = 0 was meant, and doubling the time to the highest point.
How do I solve questions with two particles?
Write each particle's displacement formula on separate lines with its own time. Common errors are using the same time expression for both, using T + 1 instead of T − 1, and forgetting that the second particle starts later.
What is the velocity-time graph mistake examiners mention?
Assuming the graph is made of straight lines, then finding areas with triangles and trapezia without integration. Annotate graphs clearly, with axes, times and velocities labelled.
Practice this topic
Ready to try some? Work through past paper questions on this topic one at a time. Attempt each question fully first, and open the mark scheme only afterwards.