What is acceleration and how to calculate it

Acceleration is the rate of change of velocity. It is not "going fast" — it is changing speed. A car cruising at 120 mph has zero acceleration; a car pulling away from a light at 12 mph is accelerating far more.

The formula

a = (v − v₀) ÷ t

Where v₀ is the initial velocity, v the final one and t the elapsed time. The unit is m/s² — metres per second, per second: how many m/s the velocity gains with each passing second.

Acceleration is a vector: it has magnitude and direction. That means braking is acceleration (with the opposite sign), and that taking a corner at constant speed is also acceleration, because the direction of motion changes. It is why you get pushed sideways in a bend without the speedometer moving.

Worked example

A car goes from 0 to 60 mph in 7 seconds. What is the average acceleration?

1. Convert to m/s: 60 mph = 26.82 m/s
2. a = (26.82 − 0) ÷ 7 = 3.83 m/s²

So each second the car gains nearly 4 m/s (8.6 mph) of speed.

Comparing to gravity: the "g" scale

The most intuitive way to feel an acceleration is against gravity, g = 9.8 m/s². Divide the value by 9.8 and you get how many "g" you are experiencing:

Situation	Acceleration	In g
Ordinary car, 0–60 in 7 s	3.83 m/s²	0.39 g
Sports car, 0–60 in 3 s	8.94 m/s²	0.91 g
Free fall	9.8 m/s²	1.0 g
Emergency braking (60 → 0 in 130 ft)	9.07 m/s²	0.93 g
Roller coaster (typical peak)	~39 m/s²	~4 g

The figure that surprises people is the fourth row: an ordinary car brakes harder than a sports car accelerates. Modern tyres and brakes dissipate energy far faster than an engine can supply it, which is why emergency braking throws your body forward with a force no launch reproduces.

Acceleration, speed and distance

With constant acceleration, three formulas solve almost everything:

• v = v₀ + a·t — velocity as a function of time
• s = v₀·t + a·t² ÷ 2 — distance covered
• v² = v₀² + 2·a·s — velocity as a function of distance (no time needed)

The third is the most useful in traffic, because it describes braking. Since velocity is squared, stopping distance grows with the square of speed: going from 30 to 60 mph quadruples the braking distance — before adding the distance covered during reaction time, which grows only linearly.

Cornering is acceleration too

This point is worth insisting on, because it is the source of half the exam errors and a good share of the crashes in bends. A car holding a steady 40 mph around a roundabout is accelerating the whole time, because the velocity vector's direction changes at every instant.

That acceleration points at the centre of the curve and equals a = v² ÷ r, where r is the radius. On a 160-foot-radius curve at 40 mph, that comes to 6.6 m/s², or 0.67 g of lateral force.

And again, speed is squared: taking the same corner at 50 mph instead of 40 demands 56% more tyre grip. Which is why a bend taken "only slightly faster" than usual can exceed the friction limit abruptly, with no progressive warning.

Frequently asked questions

Is negative acceleration the same as deceleration? In practice yes, when the object is slowing. But the sign depends on your chosen reference: a car reversing and picking up speed has negative acceleration and is speeding up. The sign indicates direction, not "braking".

Why is the unit m/s²? Because acceleration is velocity (m/s) divided by time (s), and m/s ÷ s = m/s². Reading the unit aloud — "metres per second, every second" — usually clears the confusion for good.

What is the difference between average and instantaneous acceleration? The average uses the whole interval; the instantaneous is the value at one point. In a car's 0–60, instantaneous acceleration is far higher in first gear than in fourth — the 3.83 m/s² average hides that variation.

How much can the human body take? It depends heavily on duration and direction. A few sustained g for several seconds already causes loss of peripheral vision; trained fighter pilots handle about 9 g in a pressure suit. Impacts lasting thousandths of a second in a crash can exceed 50 g and be survivable — what matters is not just the peak but how long it acts. All the engineering of crumple zones and airbags exists to stretch that time out.