\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)
Chapter 3: Linear Motion
5.

Acceleration

Aside

Physicists think that cars have at least four accelerators, not just the one. Can you name them?
Acceleration
\(\vec a\)
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 $60 \u{mi/hr/s}$ 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 $27\u{m/s^2}$.

Note

The unit Newton is equal to \(\mathrm{kg\cdot m\over s^2}\) which is why $\u{N/kg}$ is the same as $\u{m/s^2}$.

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

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

That means that every second an object is falling, its speed increases by $9.8\u{m/s}$. 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.