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)