About this chapter
Constant acceleration is the foundation of Mechanics 1. The five suvat formulae and velocity-time graphs come back in every later chapter, so this is where good habits start: a sketch, a positive direction, g = 9.8 and answers to two or three significant figures.
This chapter covers units, the suvat formulae, directions and signs, velocity-time graphs, multi-stage journeys, vertical motion under gravity, two objects that meet, quadratics with a root to reject, and other motion graphs. The later questions include a skydiver, a bouncing ball whose heights form a geometric sequence, and two cars in parallel lanes.
The ten questions
- Q1 (6 marks): a car speeds up from u to 2.5u over 84 m: find u, the acceleration, and a distance.
- Q2 (6 marks): a ball thrown up from 19.6 m above the ground: its landing speed and time of flight.
- Q3 (7 marks): a train between two stations: a speed-time graph, the time at constant speed, and the average speed.
- Q4 (6 marks): a cyclist's displacement-time graph turned into velocities, averages and a velocity-time graph.
- Q5 (6 marks): the greatest height of a ball, and how long it stays at least 19.6 m up.
- Q6 (10 marks): a two-stage journey gives 5V² − 63V − 180 = 0, with one root rejected.
- Q7 (10 marks): a ball rebounding at half speed: bounce heights as a geometric sequence and their total.
- Q8 (10 marks): a skydiver in free fall, then decelerating, then at constant speed, with a root to reject.
- Q9 (10 marks): one ball thrown up and one dropped at the same instant: when and where they collide.
- Q10 (11 marks): two cars' velocity-time graphs: the greatest gap and when one draws level.
Key skills tested
Units. Work in metres and seconds: 1 km = 1000 m, and 36 km/h = 10 m/s. Give units with every answer.
The suvat formulae. v = u + at, s = ½(u + v)t, s = ut + ½at², s = vt − ½at² and v² = u² + 2as. List s, u, v, a and t before choosing one.
Direction and signs. Choose a positive direction. A deceleration is a negative a, but give its size as a positive answer. Displacement is not the same as distance.
Velocity-time graphs. The gradient is the acceleration and the area is the distance. Use straight lines only, with no solid vertical lines, and label values on both axes.
Multi-stage motion. The final velocity of one stage is the initial velocity of the next. Keep a separate time for each stage.
Vertical motion. With up as positive, a = −9.8 m/s² throughout the flight, and v = 0 at the top. After using g = 9.8, give 2 or 3 significant figures.
Two objects. Write each displacement from the same point in terms of the same t, then set them equal to find when they meet or draw level.
Quadratics. Solve fully, then reject a root that is negative or outside the stage, giving a reason in context.
Other motion graphs. On a displacement-time graph the gradient is velocity. Average speed is total distance ÷ total time.
Worked example
Question 1 from this chapter. A car passes P with speed u m/s and, 6 seconds later, passes Q with speed 2.5u m/s. PQ = 84 m. Find (a) u, (b) the acceleration, and (c) the distance from P when the speed is 14 m/s.
(a) Using s = ½(u + v)t: 84 = ½(u + 2.5u) × 6 = 10.5u, so u = 8.
(b) The speed goes from 8 to 20 in 6 s, so a = 12 ÷ 6 = 2 m/s².
(c) Using v² = u² + 2as: 14² = 8² + 2 × 2 × s, so 196 − 64 = 4s and s = 33 m.
Listing s, u, v, a and t first makes the right formula obvious each time.
Seen on real papers
Every question in our booklets is original. These are the recent papers where each question type has appeared.
- January 2025, Q2: a two-stage journey drawn as a speed-time graph, leading to a quadratic in V with one root rejected, as in Q6.
Where marks are lost
- A solid vertical line. In January 2025 a few drew a solid vertical line on the speed-time graph and lost a mark.
- Keeping both roots. A small number did not reject the other root of the quadratic and lost the accuracy mark.
- A negative deceleration. A substantial number gave the deceleration as a negative number, which cost a mark: a deceleration is a size.
- Misreading the times. Many treated the total time of both stages as the time for one stage. Answers bigger than the whole journey time should have been a warning sign.
Common questions
Should I use g = 9.8 or 9.81?
9.8, as stated on the front of the paper, then give answers to 2 or 3 significant figures.
Which suvat formula should I use?
Write down which of s, u, v, a and t you know and which you need. The formula that uses exactly those is the one.
How do I get a distance from a velocity-time graph?
Find the area under the graph, splitting it into triangles, rectangles or trapezia.
Where this chapter leads
- Mechanics 1 Chapter 4: Dynamics of a Particle Moving in a Straight Line: accelerations from F = ma, used with suvat.
- Mechanics 1 Chapter 3: Vectors in Mechanics: motion with constant velocity in two dimensions.