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Ratio, proportion & rates of change · Compound units & rates

Chapter 1 · 3

The idea

Kinematics formulae (constant acceleration)

Three printed formulae, v = u + at, s = ut + ½at² and v² = u² + 2as, answer every question about steady acceleration in a straight line. What the five letters mean, how to pick the formula that leaves out the letter you don't need, how to rearrange for a, u, s or t, what a negative value is telling you, and how to join two stages of one journey.

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Ratio, proportion & rates of change · Compound units & rates

Kinematics formulae (constant acceleration)

Three printed formulae, v = u + at, s = ut + ½at² and v² = u² + 2as, answer every question about steady acceleration in a straight line. What the five letters mean, how to pick the formula that leaves out the letter you don't need, how to rearrange for a, u, s or t, what a negative value is telling you, and how to join two stages of one journey.

Why it works

Speeding up at a steady rate

A cyclist rolls past a lamp post at 33 m/s and pedals harder, so that her speed rises by 0.50.5 m/s every second for 1010 seconds. How fast is she going at the end, and how far has she gone?

Distance == speed ×\times time, the constant-speed rule, cannot answer that: her speed never stays the same. What does stay the same is the rate it changes, 0.50.5 m/s every second. That rate is her acceleration, written 0.50.5 m/s² ("metres per second, per second"). This page is about straight-line motion with a constant acceleration, and this cyclist rides through all of it.

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