Question

Consider the equation y=mt+b, where the dimension of y is length and the dimension of t is time, and m and b are constants.

(a) What are the dimensions and SI units of m?

a) [L/T]
b) [L/T²]
c) [L]
d) [T/L]

Answer 1

The dimensions of m in the equation y = mt + b are [L/T] and its SI units are meters per second (m/s). The dimension of b is [L] and its SI units are meters (m).

Step-by-step explanation:

The equation y = mt + b, given that y represents length and t represents time, is used to describe a linear relationship where y changes over time t. The coefficient m represents the slope of this line, which is the rate of change of length per unit time, so the dimension of m is length divided by time, which is represented as [L/T]. In SI units, this is measured in meters per second (m/s). The constant b represents the y-intercept, which is the value of y when t equals 0, thus it has the dimension of length [L] and in SI units is measured in meters (m).