To show that the equation for impulse, Ft = m(v - u), is dimensionally correct, we need to analyze the dimensions of each term in the equation.
Let's break down the dimensions of each term:
F: Force (dimension: [M][L][T]^-2) t: Time (dimension: [T]) m: Mass (dimension: [M]) v: Final Velocity (dimension: [L][T]^-1) u: Initial Velocity (dimension: [L][T]^-1)
Now, let's substitute the dimensions into the equation and see if they are consistent:
Left-hand side (LHS): Ft = [M][L][T]^-2 [T] = [M][L][T]^-1
Right-hand side (RHS): m(v - u) = [M]([L][T]^-1 - [L][T]^-1) = [M][L][T]^-1
Both the LHS and RHS have the same dimensions of [M][L][T]^-1, which means they are consistent.
Therefore, the equation Ft = m(v - u) is dimensionally correct.