Acceleration is the rate at which speed changes. In SI units it's measured in metres per second per second, written m/s²: an acceleration of 1 m/s² adds one metre per second of speed every second. The other unit people meet most is g, standard gravity, which was fixed by international agreement in 1901 at exactly 9.80665 m/s². In feet, that's about 32.17 ft/s². Because g is a fixed number rather than the local pull of gravity, which varies slightly around the Earth, conversions between g and m/s² are exact.
Where you meet it in the UK
Most people encounter acceleration through cars. UK car reviews quote 0-62 mph times, because 62 mph is almost exactly 100 km/h, the standard European test. Deceleration matters just as much, and the Highway Code's stopping distances contain it implicitly. At 70 mph, the Code gives a braking distance of 75 metres once the brakes are applied. Seventy miles an hour is about 31.3 m/s, and stopping from that speed in 75 metres requires an average deceleration of about 6.5 m/s², or roughly two-thirds of a g. That figure assumes a dry road, good tyres and an alert driver. On a wet road, braking distances can double, which means the car can only manage about a third of a g.
Precision and rounding pitfalls
The commonest mistake is treating a quoted figure as constant. A 0-62 mph time gives an average acceleration, but cars pull hardest in the lower gears and much less near the top of the run, so peak acceleration can be far higher than the average. The second mistake is mixing speed units in the middle of a calculation. Convert mph or km/h to metres per second first: multiply mph by 0.44704, or divide km/h by 3.6. Only then divide by time.
Worked conversions
A roller coaster that pulls 4 g at the bottom of a drop is producing about 39.2 m/s², or around 129 ft/s². A lift that reaches its speed with an acceleration of 1.2 m/s² is applying about 0.12 g, which is why you feel slightly heavier as it starts going up. And a cyclist braking from 20 mph, about 8.9 m/s, to a stop in 5 metres needs an average deceleration of about 7.9 m/s², a little over 0.8 g, which is close to the limit before the rear wheel lifts or skids.
Acceleration and comfort
Engineers who design trains, lifts and buses work hard to limit acceleration, because passengers notice it long before it becomes dangerous. Most people find a steady acceleration of around 1 to 1.5 m/s² comfortable when standing, roughly 0.1 to 0.15 g. Sudden changes in acceleration, called jerk, are what make a journey feel rough, which is why a smooth driver eases on and off the brakes rather than applying them firmly at the last moment.
Checking your answer
Two reference points catch most mistakes. Ordinary driving almost never exceeds 1 g: a family car accelerating briskly reaches about 0.3 g, and hard braking on a dry road about 0.7 to 0.8 g. If a conversion gives a car several g, a unit has slipped, most often mph left unconverted in a calculation that expects metres per second. And free fall near the Earth's surface is about 9.8 m/s²; if a falling object appears to accelerate faster than that, check the arithmetic.
One more worked example
A train accelerating from a station at a steady 0.8 m/s² reaches 100 km/h, about 27.8 m/s, in roughly 35 seconds, covering around 480 metres while it does so. In g terms that's about 0.08 g, gentle enough that standing passengers barely need to hold on. The same calculation explains why rail timetables lose so much time to stopping and starting: each stop costs not just the dwell time at the platform, but the time spent slowing down and speeding up again.