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 how to find the displacement of the car by calculating the area under its velocity-time graph: Step 1: Convert time units and identify the motion phases. The car moves for 2 minutes at constant velocity, and then for 6 seconds with constant acceleration. First, convert 2 minutes to seconds: t_1 = 2 minutes × 60 s/minute = 120 s The total time interval is 120 s + 6 s = 126 s. Step 2: Calculate the displacement during the constant velocity phase (0 to 120 s). During this phase, the velocity is constant at v = 6 m s^-1. On a velocity-time graph, this is represented by a horizontal line from t=0 to t=120 s at v=6 m s^-1. The area under this segment is a rectangle. s_1 = velocity × time s_1 = 6 m s^-1 × 120 s = 720 m Step 3: Calculate the displacement during the acceleration phase (120 s to 126 s). At the start of this phase (at t=120 s), the initial velocity is u = 6 m s^-1. The acceleration is a = 1 m s^-2 for t_2 = 6 s. First, calculate the final velocity v at t=126 s: v = u + at_2 v = 6 m s^-1 + (1 m s^-2 × 6 s) v = 6 m s^-1 + 6 m s^-1 = 12 m s^-1 On a velocity-time graph, this phase is represented by a straight line sloping upwards from (120 s, 6 m s^-1) to (126 s, 12 m s^-1). The area under this segment is a trapezium. The displacement s_2 is the area of this trapezium: s_2 = (1)/(2)(u + v)t_2 s_2 = (1)/(2)(6 m s^-1 + 12 m s^-1) × 6 s s_2 = (1)/(2)(18 m s^-1) × 6 s s_2 = 9 m s^-1 × 6 s = 54 m Step 4: Calculate the total displacement. The total displacement is the sum of the displacements from both phases. S_total = s_1 + s_2 S_total = 720 m + 54 m = 774 m The total displacement of the car is 774 m. That's 3 down. 2 left today — send the next one.