Acceleration

1. Acceleration is how quickly the velocity of an object changes, so an object accelerates when it speeds up, slows down or changes direction.
2. You recall acceleration from $acceleration=\frac{change\; in\; velocity}{time}$, written in symbols as $a=\frac{v-u}{t}$.
3. Acceleration is measured in metres per second squared, ${m/s}^2$, and an acceleration of $2{m/s}^2$ means the velocity changes by $2m/s$ every second.
4. When an object slows down, $v$ is smaller than $u$, so the acceleration is negative and is called a deceleration.
5. The magnitude of an acceleration is its size without its direction, so a car slowing at $-4{m/s}^2$ has an acceleration of magnitude $4{m/s}^2$.
6. A large acceleration needs a large change in velocity, a short time, or both.
7. A fast object does not have to be accelerating, because a car moving at a steady $30m/s$ in a straight line has zero acceleration.

Estimating an acceleration

1. To estimate an acceleration, you choose sensible rounded values for the change in velocity and the time taken, then divide one by the other.
2. Typical speeds give the change in velocity, so a car pulling away from traffic lights and reaching town speed changes its velocity by about $13m/s$.
3. The time comes from everyday experience, such as how many seconds a car takes to reach that speed.
4. The answer is rounded to one significant figure, because the starting values are only estimates.
5. A useful benchmark is the acceleration of an object in free fall near the Earth's surface, which is about $10{m/s}^2$.
6. Comparing an estimate with $10{m/s}^2$ quickly shows whether it is sensible, because most everyday accelerations are smaller than this.

Typical everyday accelerations

1. Starting to walk: a person reaches $1.5m/s$ in about $1s$, so the acceleration is roughly $1.5{m/s}^2$.
2. Sprint start: an athlete leaving the blocks reaches about $10m/s$ in about $2s$, giving roughly $5{m/s}^2$.
3. Cycling: a cyclist pulling away reaches about $6m/s$ in about $4s$, giving about $1.5{m/s}^2$.
4. Family car: a car pulling away normally reaches about $13m/s$ in around $5s$, giving about $3{m/s}^2$.
5. Bus or train: these speed up more gently, at about $1{m/s}^2$ or less, so that standing passengers keep their balance.
6. Lift: a lift starting or stopping accelerates at about $1{m/s}^2$, which is why you feel slightly heavier or lighter for a moment.
7. Car braking: a car braking normally slows at about $3{m/s}^2$, and in an emergency stop on a dry road its deceleration can reach about $7{m/s}^2$.
8. Falling object: an object in free fall accelerates at about $10{m/s}^2$, which is larger than almost every acceleration you experience in normal travel.