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
Step 1: Find the initial velocity of the body (u). We are given the acceleration (a), final velocity (v), and time (t). We can use the first equation of motion: v = u + at Given: a = 12\,m/s^2 v = 80\,m/s t = 5\,s Substitute the values into the equation: 80\,m/s = u + (12\,m/s^2)(5\,s) 80 = u + 60 Subtract 60 from both sides to solve for u: u = 80 - 60 u = 20\,m/s The initial velocity of the body is 20 m/s. Step 2: Find the distance covered in the 9th second. The distance covered in the n^th second is given by the formula: S_n = u + (a)/(2)(2n - 1) Here, n = 9 (for the 9th second). We use the initial velocity u = 20\,m/s (found in Step 1) and the acceleration a = 12\,m/s^2. Substitute the values into the formula: S_9 = 20\,m/s + (12\,m/s^2)/(2)(2 × 9 - 1) S_9 = 20 + 6(18 - 1) S_9 = 20 + 6(17) S_9 = 20 + 102 S_9 = 122\,m The distance covered in the 9th second is 122 m.