The Velocity Function in One Dimension
Units
The velocity function has dimensions of length/time, [L/T]. In SI units, this is meters/seconds, \(m/s\). Note that the input to the velocity function is time, which has dimensions of time (shocker!) and units of seconds in SI.
For example, for $$v(t) = 2 + 3t + 4t^2 $$ \(v(t)\) has units of \(m/s\), 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 (and dimensions). In SI for this example, 2 has units of \(m/s\), 3 has units of \(m/s^2\), and 4 has units of \(m/s^3\).
Some books will include the units of constants with formulae. In this case, the above would be written as, $$v(t) = 2(m/s) + 3(m/s^2)t + 4(m/s^3)t^2 $$ 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.