Question

Consider the equation y = mt + b, where the dimensions of y is length and the dimensions of t is time, and m and b are constants. When answering question parts in this problem, use the symbols L and T to represent dimensions of length and time, respectively, and use the symbols m and s to represent the SI units of meters and seconds, respectively.

Answer 1

Answer: SI unit of 'b' is meter (m) while 'm' is m/s.

dimension of 'm' is [L$T^{-1}$] and 'b' is [L]

Explanation:

consider the equation

y = mt + b      ................ (1)

where y represent the length with a dimension of [L]

also t represent the time with a dimension of [T]

so from (1) we can say that the dimension of mt must equal the dimension of y.

thus

[mt] = [L]

which is [m] = [L$T^{-1}$]

• so the dimension of m becomes [L$T^{-1}$]

• from the unit of y which is meter  and time t in second

      the unit of m = meter/ second = m/s

so the S I unit of 'm' is m/s

• Also from (1) we can say that the dimension of 'b' is equal to the dimension of y.

so [b] = [L]

so, dimension of b is [L]

• SI unit of b is meter (m)

Answer 2

The SI unit for b is meter represented by 'm' and for m is meter per second which is represented by 'm/s'.

The dimension for 'm' is represented by [$\rm LT^{-1}$] and for 'b' is represented by  [L]

SI Units

The International System of Units is a scientific method of expressing the magnitudes or quantities of important natural phenomena.

The equation given is,

y = mt + b

In the above-given equation, y is represented by the dimensions of length and t is represented by the dimensions of time. These can be written as below.

Dimension of y = L and Dimension of t = T

From the above equation, the dimensions of both sides of the equation will be equal. Hence the dimension of 'mt' will be same as the dimension of y.

Dimension of 'mt' = L

Dimension of 'm' = [$\rm LT^{-1}$]

Now the SI unit of y is meter and for time t is second. Hence the SI unit for m is meter per second.

SI Unit of 'm' = m/s.

Similarly, the dimensions of b is the same as the dimensions of y. Hence

Dimension of 'b' = L

SI unit of 'b' = meter= m.

Hence we can conclude that the dimension of 'm' is represented by [$\rm LT^{-1}$] and for 'b' is [L]. The SI unit for 'm' is 'm/s' and for 'b' is 'm'.

To know more about the SI unit, follow the link given below.

https://brainly.com/question/24688141.