## In the equation z = ct d, z is measured in meters and t is measured in seconds. what are the dimensions (units) of c?

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In the equation z = ct d, z is measured in meters and t is measured in seconds. what are the dimensions (units) of c?

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6 days 2022-12-30T23:52:49+00:00 2 Answers 0 views 0

1. In the equation z = c t + d, where z is measured in meters (m) and t is measured in seconds (s), the dimensions of c are meters / seconds which can also be expressed as m / s.
We are given the equation z = c t + d;
where z is measured in meters and t is measured in seconds. T
We have to find the dimension or units of c.
Dimensions means some physical quantities that exist in some particular domains of existence and can be measured.
If we have a equation, then the dimension that is on the left sides of it should be the same as the one on the right on it.
This is called the homogeneity of dimensions for an equation that is being given.
Now, we have the equation:
z = c t + d
Since,
z is being measured in meters (m), so by using the principle of homogeneity of dimensions, c t must also be measured in meters (m).
Also, t is measured in seconds (s).
So, if the dimensions of c are meters/second then the term c t will be measured in meters.
Therefore, the dimensions of c are meters/second or m / s.
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2. In the equation z = c t + d, where z is measured in meters (m) and t is measured in seconds (s), the dimensions of c are meters/seconds or m / s
Given: The equation z = c t + d, where z is measured in meters and t is measured in seconds. To find the dimensions of c
What are the units and dimensions?
Dimensions can be defined as some physical quantities that exist in some particular domains of existence that can be measured, whereas units are just some arbitrary names that are reserved by particular dimensions which are used to define the quantity that is about the measurement or the dimensions used concerning the particular object or instance of something.
What is the homogeneity of dimensions?
In a given equation consisting of different variables, the dimensions assigned with each term in the equation must be consistent on both the left and right sides.
For example: Let’s take the formula of final velocity (v):
v = u + a t, where
v = final velocity and unit is m / s
u = initial velocity and unit is m / s
a = linear acceleration and unit is m / s²
t = time and unit is t
Observe the dimension and units for each term in the equation.
On the left-hand side, we have only one term which is v  (final velocity) and is measured in m / s.
On the right-hand-side, we have 2 terms u (initial velocity) and at (acceleration and time)
u is measured in m / s
a is measured in m / s² and t is measured in s
so, it is measured in m / s² × s is m / s
Therefore both u and at has the dimensions as m / s.
Hence all the terms in LHS and RHS which are v, u, and at are measured in m / s.
This is known as the homogeneity of dimensions for an equation.
Let’s solve the given equation:
z = c t + d
where z is measured in meters and t is measured in seconds.
Now z is measured in meters (m), so by the principle of homogeneity of dimensions, c t must also be measured in meters (m).
Now t is measured in seconds (s), so if the dimensions of c are meters/second then the term c t will be measured in meters.
Hence the dimensions of c are meters/second or m / s
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