What are the units of the function q = 1/4ct^3, where c is in m/s and t is in seconds (s)?

To determine the units of the function ( q = \frac{1}{4} ct^3 ), we need to analyze the units involved in the equation, given that ( c ) is in meters per second (m/s) and ( t ) is in seconds (s).

First, let's look at the term ( ct^3 ):

• The variable ( c ) has the units of m/s, meaning it represents a speed.

• The term ( t^3 ) means we are cubing the unit of time. Since ( t ) is in seconds, ( t^3 ) results in seconds cubed, or ( s^3 ).

Now, combining these units gives us:

[

c t^3 = \left(\frac{\text{m}}{\text{s}}\right)(\text{s}^3)

]

When multiplying these units, we can simplify:

[

\frac{\text{m} \cdot \text{s}^3}{\text{s}} = \text{m} \cdot \text{s}^2

]

This simplifies to m × s².

Therefore, the function ( q ) ultimately has the units of