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
Fresh day Stars, let's solve. Problem 1: Moving object a) Find the acceleration of the object when t=3. Step 1: Identify the segment of the graph. From t=0 to t=5 seconds, the speed-time graph is a straight line. The acceleration is constant in this interval. The points on the graph for this segment are (0,0) and (5,24). Step 2: Calculate the acceleration. Acceleration is the gradient of the speed-time graph. Acceleration = Change in speedChange in time = 24\, m/s - 0\, m/s5\, s - 0\, s Acceleration = (24)/(5)\, m/s^2 = 4.8\, m/s^2 The acceleration when t=3 is 4.8 m/s^2. b) Given that the object decelerates at 2\, m/s^2, find the value of t. Step 1: Identify the deceleration segment. Deceleration occurs in the last segment of the graph, from t=15 seconds to t. At t=15 seconds, the speed is 24\, m/s. At time t, the speed is 0\, m/s (as the graph ends on the time axis). Deceleration of 2\, m/s^2 means the acceleration is -2\, m/s^2. Step 2: Use the acceleration formula to find t. Acceleration = Final speed - Initial speedFinal time - Initial time -2\, m/s^2 = 0\, m/s - 24\, m/st\, s - 15\, s -2 = (-24)/(t - 15) Step 3: Solve for t. -2(t - 15) = -24 t - 15 = (-24)/(-2) t - 15 = 12 t = 12 + 15 t = 27\, s The value of t is 27 s. c) Calculate the average speed of the object in the first 10 seconds of the journey. Step 1: Calculate the total distance covered in the first 10 seconds. The distance is the area under the speed-time graph. From t=0 to t=5 seconds, the shape is a triangle: Area_1 = (1)/(2) × base × height = (1)/(2) × 5\, s × 24\, m/s = 60\, m From t=5 to t=10 seconds, the shape is a rectangle: Area_2 = width × height = (10\, s - 5\, s) × 24\, m/s = 5\, s × 24\, m/s = 120\, m Total distance = Area_1 + Area_2 = 60\, m + 120\, m = 180\, m. Step 2: Calculate the average speed. Average speed is total distance divided by total time. Average speed = Total distanceTotal time = 180\, m10\, s = 18\, m/s The average speed in the first 10 seconds is $*18 m/