Question

Question: 1. Which of the equations below are dimensionally correct? (where v is velocity, x is position, a is acceleration, and t is time) 1 x b) v = v.- 2a(x; - x)

Answer 1

To determine whether the equations are dimensionally correct, we need to analyze the dimensions of each term in the equations.

1. For the equation \( v = v_0 + 2a(x_f - x_i) \):

- \( v \) has the dimension of velocity \([L T^{-1}]\).
- \( v_0 \) also has the dimension of velocity \([L T^{-1}]\).
- \( a \) has the dimension of acceleration \([L T^{-2}]\).
- \( x_f - x_i \) represents a change in position, and has the dimension of length \([L]\).

Now, let's analyze the right side of the equation:

- The term \( 2a(x_f - x_i) \):
- \( a \) has units of \([L T^{-2}]\).
- \( (x_f - x_i) \) has units of \([L]\).
- Therefore, \( a(x_f - x_i) \) has the dimension \([L T^{-2}] \times [L] = [L^2 T^{-2}]\).

So, the unit analysis for the right side \( v_0 + 2a(x_f - x_i) \) becomes:

- The term \( v_0 \) has units of \([L T^{-1}]\).
- The term \( 2a(x_f - x_i) \) has units of \([L^2 T^{-2}]\).

Because the dimensions are not consistent on both sides of the equation, **the equation is dimensionally incorrect.**

In summary, the provided equation \( v = v_0 + 2a(x_f - x_i) \) is not dimensionally correct.

If you have another equation or need clarification on the terms, please provide more detail, and I will assist you accordingly!