Study case: solving a constant acceleration motion problem In this A-Level Mechanics Constant Acceleration Problem Tutor, I use one study case to show how I teach SUVAT questions in a calm and organised way. The problem is: a car starts from rest and accelerates uniformly at 3 m/s^2 for 8 seconds. Find the final velocity and the distance travelled. This is a useful example because it contains the key mechanics habit that many students need: list the variables first, choose the right equation second, and only then calculate. The final answers are 24 m/s for the velocity and 96 m for the distance. Before solving, I ask the student to translate the wording into mechanics notation. Starts from rest means u = 0. Accelerates uniformly at 3 m/s^2 means a = 3. The time is t = 8. We need final velocity v and displacement s. I encourage students to write a clear SUVAT list because it reduces panic and prevents them from selecting equations randomly. A good variable list is often half the solution. Method 1 is the direct velocity equation. To find final velocity, I use v = u + at. Substituting gives v = 0 + 3 times 8 = 24. So the final velocity is 24 m/s. I explain that this result is sensible because the car gains 3 m/s every second for 8 seconds. This mental interpretation helps the student see the meaning of acceleration rather than treating it as only a letter in a formula. To find distance in Method 1, I use s = ut + 1/2 at^2. Substituting gives s = 0 times 8 + 1/2 times 3 times 8^2. This is 1.5 times 64, which gives 96. So the distance travelled is 96 m. I ask the student to include units because mechanics answers without units can look unfinished and can lose clarity in longer problems. Method 2 is the average velocity method. When acceleration is constant, the average velocity is (u + v)/2. We already know u = 0 and v = 24, so the average velocity is 12 m/s. Distance equals average velocity times time, so s = 12 times 8 = 96 m. This method is helpful because it explains why the displacement is not simply 24 times 8. The car is not travelling at 24 m/s for the whole time; it gradually speeds up from 0 to 24. Method 3 is a velocity-time graph check. I draw a graph with time on the horizontal axis and velocity on the vertical axis. The graph is a straight line from 0 m/s at t = 0 to 24 m/s at t = 8. The distance travelled is the area under the velocity-time graph. That area is a triangle with base 8 and height 24, so the area is 1/2 times 8 times 24 = 96. This visual method is powerful because it connects SUVAT with graphs and helps students understand displacement as area under a velocity-time graph. After the three methods, I compare them. The SUVAT equation is usually the fastest exam method. The average velocity method is elegant when acceleration is constant. The graph method gives the deepest visual understanding. I want the student to see that all three routes are consistent. When several methods lead to the same answer, confidence improves, and the student is less likely to feel that mechanics is just a collection of disconnected formulae. Common mistakes include using final velocity as if it were the average velocity, forgetting that the initial velocity is zero, using t instead of t^2 in the displacement formula, and missing units. Another common problem is choosing an equation that contains an unknown the student does not need. I teach students to look at which variables are known and which variable is required before selecting the formula. This turns equation choice into a logical decision. I also show how the same question could become harder. The car might start with an initial velocity, the acceleration might be negative, or the question might ask how long it takes to reach a certain speed. Sometimes the motion has two stages, such as accelerating and then braking. In those cases, the student must keep the information for each stage separate. The simple study case is the foundation for those harder questions. A useful extension is: a car starts from rest, accelerates at 3 m/s^2 for 8 seconds, then travels at constant speed for another 5 seconds. Find the total distance. This adds a second stage and encourages the student to use the first result as a bridge. I introduce this only after the student can solve the original problem confidently. In one-to-one tutoring, I would finish by giving the student a similar SUVAT question with changed numbers. Then I would ask them to explain why they chose each equation. My goal is not for the student to memorise one example; my goal is for them to develop a repeatable structure: list variables, choose an equation, substitute carefully, calculate, check units and interpret the answer. For support with this topic, students can book one-to-one tutor services: https://www.mastermathstutoring.co.uk/services. 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