Estimating Accelerations

Velocity is speed in a specified direction. For everyday motion along a straight line, we can estimate acceleration by considering how much the speed increases or decreases over a few seconds.

An acceleration of $2\text{ m/s}^2$ means that velocity changes by $2\text{ m/s}$ each second. If this acceleration stays constant as an object speeds up from rest, its speed will be about $2\text{ m/s}$ after one second and $4\text{ m/s}$ after two seconds.

Estimating an acceleration

To estimate average acceleration, choose reasonable values for the initial velocity, final velocity and time taken:

Here, $u$ is the initial velocity and $v$ is the final velocity, both in m/s; $t$ is the time in seconds. The answer is in m/s².

A typical family car might take around 10 seconds to accelerate from rest to 27 m/s, roughly 60 mph. Its average acceleration is therefore:

This gives a useful benchmark: a family car accelerating briskly has an acceleration of roughly 2–3 m/s². The calculated value is an average over the ten seconds; it does not mean that the acceleration is exactly the same throughout.

For the same change in velocity, taking less time means a greater acceleration. For the same time interval, a larger change in velocity also means a greater acceleration.

Making sense of the magnitude

The magnitude of an acceleration is its size, without a direction or minus sign. Slowing down counts as acceleration too, because velocity is changing.

Suppose a bicycle travelling in a straight line slows from $6\text{ m/s}$ to rest in $3\text{ s}$. Taking its original direction of travel as positive, its average acceleration is $(0-6)/3 = -2\text{ m/s}^2$. The minus sign shows that the acceleration acts against its motion. Its acceleration has a magnitude of 2 m/s².

Another useful comparison is an object falling near Earth's surface. When air resistance is negligible, its downward acceleration is about 10 m/s²: its downward speed increases by about 10 m/s each second. This is several times the family-car benchmark.

These comparisons help you judge whether an estimate is sensible. An acceleration of a few m/s² is plausible for a car speeding up; hundreds of m/s² would be far above that everyday benchmark. An estimate should match the situation, not merely produce a number.