To determine the units of [tex]\( c \)[/tex] in the equation [tex]\( z = c \cdot t + d \)[/tex], we need to carefully analyze the units involved in each term of the equation.
1. Given Units:
- [tex]\( z \)[/tex] is measured in meters (m).
- [tex]\( t \)[/tex] is measured in seconds (s).
- [tex]\( d \)[/tex] is a constant and, like [tex]\( z \)[/tex], is measured in meters (m).
2. Isolate [tex]\( c \)[/tex]:
We can rearrange the equation [tex]\( z = c \cdot t + d \)[/tex] to better understand the units of [tex]\( c \)[/tex].
[tex]\[
z - d = c \cdot t
\][/tex]
Since [tex]\( z \)[/tex] and [tex]\( d \)[/tex] are both in meters, [tex]\( z - d \)[/tex] will also be in meters (m).
3. Solve for [tex]\( c \)[/tex]:
[tex]\[
c = \frac{z - d}{t}
\][/tex]
4. Substitute Units:
- The numerator [tex]\( z - d \)[/tex] has the units of meters (m).
- The denominator [tex]\( t \)[/tex] has the units of seconds (s).
[tex]\[
c = \frac{\text{meters}}{\text{seconds}} = \frac{m}{s}
\][/tex]
Therefore, the units of [tex]\( c \)[/tex] are meters per second (m/s). [tex]\(\boxed{\frac{m}{s}}\)[/tex]
