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: Determine the acceleration from the first interval. The object starts from rest, so its initial velocity u = 0. It moves with a constant acceleration, let's call it a. In the first 2 seconds (t_1 = 2 s), it covers a distance s_1 = s. We use the kinematic equation: s = ut + (1)/(2)at^2. For the first 2 seconds: s_1 = u t_1 + (1)/(2) a t_1^2 s = (0)(2) + (1)/(2) a (2)^2 s = 0 + (1)/(2) a (4) s = 2a From this, we can express the acceleration a in terms of s: a = (s)/(2) Step 2: Calculate the total distance traveled in the first 4 seconds. The "next 2 seconds" means the interval from t=2 s to t=4 s. So, we need to find the total distance traveled from t=0 to t=4 s. Let S_total be the total distance covered in t_total = 4 s. Using the same kinematic equation with u=0 and a = (s)/(2): S_total = u t_total + (1)/(2) a t_total^2 S_total = (0)(4) + (1)/(2) ((s)/(2)) (4)^2 S_total = 0 + (1)/(2) ((s)/(2)) (16) S_total = (16s)/(4) S_total = 4s Step 3: Find the distance traveled in the next 2 seconds. The distance traveled in the next 2 seconds (s_next) is the total distance traveled in 4 seconds minus the distance traveled in the first 2 seconds. s_next = S_total - s_1 s_next = 4s - s s_next = 3s The object will travel 3s meters in the next 2 seconds. The final answer is 3s.