Acceleration

Aside

Physicists think that cars have at least four accelerators, not just the one. Can you name them?

Acceleration

\vec{a}

Units:m/s²

Physicists use the term acceleration to describe any change in velocity: speeding up, slowing down, even changing direction. (We will not use the word "decelerate".) The SI units of acceleration are meters-per-second per second: that is, the acceleration is how much the velocity changes per unit of time.

For example, if a car is advertised as "going from 0 to 60 in 6 seconds" then that’s a statement about its acceleration: it takes 6 seconds to accelerate from rest to 60mi/hr. We would write that acceleration as $60 mi / hr / s$ or $60 \frac{mi / hr}{s}$ . In SI units, this would be $27 \frac{m / s}{s}$ . More commonly, however, we combine the two s's and write $27 m / s^{2}$ .

Note

The unit Newton is equal to

\frac{kg \cdot m}{s^{2}}

which is why

N / kg

is the same as

m / s^{2}

The standard acceleration on Earth, to which all other accelerations can be compared, is the acceleration due to gravity, which is the official name of our old friend

g = 9.8 N / kg = 9.8 m / s^{2}

That means that every second an object is falling, its speed increases by $9.8 m / s$ . If it weren't for air resistance, after three seconds a falling object would be moving at $9.8 \times 3 = 29 m / s$ , which is highway speeds! Air resistance does make a big difference when things fall, however, after about a second or so.)

An acceleration of $1 g$ is rather intense, which is why amusement park rides which just drop you from a height are so thrilling/terrifying to us. Accelerations greater than $5 g$ (sometimes referred to as "g-forces" even though they are not forces) can be dangerous to humans depending on the direction of acceleration and other circumstances.