Using dimensional analysis, which one of the following equations is dimensionally correct? ( a → m/s2, v → m/s, x → m , t → s)
x=at
To determine which equation is dimensionally correct, we need to ensure that the dimensions on both sides of the equation match.
Let's analyze each equation:
1. a = v / t
The dimensions on the left side are [a] = [m/s^2], while the dimensions on the right side are [v/t] = [m/s] / [s] = [m/s^2]. Therefore, this equation is dimensionally correct.
2. v = a * t
The dimensions on the left side are [v] = [m/s], while the dimensions on the right side are [a*t] = [m/s^2] * [s] = [m/s^2 * s] = [m/s]. Therefore, this equation is also dimensionally correct.
3. a = v * x
The dimensions on the left side are [a] = [m/s^2], while the dimensions on the right side are [v*x] = [m/s] * [m] = [m^2/s]. Therefore, this equation is not dimensionally correct.
Based on dimensional analysis, equations 1 and 2 are dimensionally correct.