This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the solution for Q.2 (a): Q.2 (a) Dimensionally prove the 1st equation of motion. The first equation of motion is given by: v_f = v_i + at where: v_f is the final velocity v_i is the initial velocity a is the acceleration t is the time To dimensionally prove this equation, we must show that the dimensions of the terms on both sides of the equation are consistent. Step 1: Determine the dimensions of each variable. Dimension of velocity (v_f, v_i): [L][T]^-1 (Length per unit Time) Dimension of acceleration (a): [L][T]^-2 (Length per unit Time squared) Dimension of time (t): [T] (Time) Step 2: Analyze the dimensions of the Left-Hand Side (LHS). The LHS is v_f. Dimension of LHS = Dimension of v_f = [L][T]^-1 Step 3: Analyze the dimensions of the Right-Hand Side (RHS). The RHS is v_i + at. First, find the dimension of the term v_i: Dimension of v_i = [L][T]^-1 Next, find the dimension of the term at: Dimension of at = (Dimension of a) × (Dimension of t) Dimension of at = ([L][T]^-2) × ([T]) Dimension of at = [L][T]^-2+1 Dimension of at = [L][T]^-1 For an equation to be dimensionally consistent, all terms added or subtracted must have the same dimensions. Here, both v_i and at have the dimension [L][T]^-1. Therefore, the dimension of the RHS (v_i + at) is also [L][T]^-1. Step 4: Compare the dimensions of LHS and RHS. Dimension of LHS = [L][T]^-1 Dimension of RHS = [L][T]^-1 Since the dimensions of the LHS and RHS are equal, the first equation of motion is dimensionally consistent. 3 done, 2 left today. You're making progress.