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Playbook

Motion in a Straight Line

The equations of motion and graphs of motion. Lighter than in the early papers; read every graph's slope and area.

Questions in the bank
103
q/paper in 2025–26
0.55
Numeric answer
27%
Notes pages
5

Tier: Long tail

When you’ll see it

A body moving along one line with a given speed, acceleration or graph, a stone thrown up or dropped, or a position written as a function of time.

How this chapter is tested

The equations of constant acceleration carry most of the chapter, on level ground or under gravity. One habit wins those marks: choose a positive direction once and give every velocity, acceleration and displacement its sign.

The rest reads a slope or an area off a graph, or differentiates a position that changes with time. When the acceleration is not constant, the three equations fail; differentiate, use a = v dv/dx, or integrate with the starting values.

This is a long-tail chapter. Marks are lost on averaging two speeds over equal distances, on forgetting the velocity a stone keeps when it leaves a rising balloon, and on taking dv/dx for the acceleration.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Average speed and relative velocity

    Average speed is total distance over total time; speeds add for bodies moving towards each other and subtract for bodies moving the same way.

  • Equations of uniform acceleration

    v = u + at, s = ut + ½at², v² = u² + 2as; pick the one that leaves out the quantity you are neither given nor asked for.

  • Motion under gravity

    Take up as positive and a = −g for the whole flight, whether the body is dropped, thrown up or thrown down.

  • Slopes and areas of motion graphs

    Slope of x–t is velocity, slope of v–t is acceleration; area under v–t is displacement, area under a–t is the change in velocity.

  • Variable acceleration

    Differentiate a position for velocity and acceleration, use a = v dv/dx when v is given against x, and integrate with the starting values.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • The plain mean of two speeds

    Over equal distances the average speed is 2v₁v₂/(v₁ + v₂). At 3 km/h and 5 km/h it is 3.75 km/h, not 4 km/h.

  • Dropped from a moving body

    A stone let go from a balloon rising at 8 m/s first rises at 8 m/s. Taking u = 0 gives a shorter fall and the wrong answer.

  • dv/dx taken as the acceleration

    dv/dx is in 1/s. The acceleration is v dv/dx, so a straight v–x line does not mean constant acceleration.

  • A turning point at a = 0

    The body reverses where v = 0. Where a = 0 the velocity is largest or smallest; and the distance across a turning point must be split there.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Motion in a Straight Line notes

Drill every Motion in a Straight Line question

103 questions from the bank, across 5 subtopics.

Drill the 103 questions

Drill one subtopic at a time

The 5 subtopics, in teaching order.

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