\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Acceleration

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 $60 \u{mi/hr/s}$ or $60\u{mi/hr\over s}$. In SI units, this would be $27\u{m/s\over s}$. More commonly, however, we combine the two s's and write $27\u{m/s^2}$.

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

That means that every second an object is falling, its speed increases by 9.8m/s. If it weren't for air resistance, after three seconds a falling object would be moving at \(9.8\times3 = 29\u{m/s}\), which is highway speeds! (Air resistance does make a big difference when things fall, however, after about a second or so.)

An acceleration of $1g$ 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 $5g$ (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.