AbrahamPhysics

Units

The acceleration function has dimensions of length/time\(^2\) [L/T\(^2\)]. In SI units, this is meters/seconds\(^2\), or
m/s\(^2\). Another way to think about this is (m/s)/s, or (meters per second, per second). For example, consider a velocity of 2 m/s. This is saying that if the velocity is constant at this value, the position would change 2 meters every second. Now consider an acceleration of 2 (m/s)/s. This is saying that if the acceleration is constnt at this value, the velocity would change 2 meters/second every second.

Remember that the input to the acceleration function is time, which has dimensions of time and units of seconds in SI. For example, for $$a(t) = 2 + 3t + 4t^2 $$ \(a(t)\) has units of m/s\(^2\), as do the terms \(2\), \(3t\), and \(4t^2\). While 2, 3, and 4 look just like regular numbers, in this case they carry units. In SI, 2 has units of m/s\(^2\), 3 has units of m/s\(^3\), and 4 has units of m/s\(^4\).

Some books will include the units of constants with formulae. In this case, the above would be written as, $$a(t) = 2(m/s^2) + 3(m/s^3)t + 4(m/s^4)t^2 $$ I do not care for this. While this does emphasize the point that the numbers have units, I think the additional notation is cumbersome and confusing. Remember dimensional analysis, and you can use it to determine which numbers or variables have units and which do not.