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
To calculate the total distance travelled by the object, we need to find the area under the velocity-time graph. The graph can be divided into four distinct geometric shapes: Step 1: Divide the graph into sections and identify the shapes. Section 1 (0 s to 6 s): A triangle. Section 2 (6 s to 9 s): A rectangle. Section 3 (9 s to 12 s): A trapezium. Section 4 (12 s to 18 s): A triangle. Step 2: Calculate the area for each section. Section 1: Triangle (0 s to 6 s) Base (b_1) = 6 s - 0 s = 6 s Height (h_1) = 20 m/s (velocity at t=6 s) Area_1 = (1)/(2) × b_1 × h_1 = (1)/(2) × 6 s × 20 m/s = 60 m Section 2: Rectangle (6 s to 9 s) Width (w_2) = 9 s - 6 s = 3 s Height (h_2) = 20 m/s (constant velocity) Area_2 = w_2 × h_2 = 3 s × 20 m/s = 60 m Section 3: Trapezium (9 s to 12 s) Parallel side 1 (v_a) = 20 m/s (velocity at t=9 s) Parallel side 2 (v_b) = 40 m/s (velocity at t=12 s) Height (h_3) = 12 s - 9 s = 3 s Area_3 = (1)/(2) × (v_a + v_b) × h_3 = (1)/(2) × (20 m/s + 40 m/s) × 3 s Area_3 = (1)/(2) × 60 m/s × 3 s = 90 m Section 4: Triangle (12 s to 18 s) Base (b_4) = 18 s - 12 s = 6 s Height (h_4) = 40 m/s (velocity at t=12 s) Area_4 = (1)/(2) × b_4 × h_4 = (1)/(2) × 6 s × 40 m/s = 120 m Step 3: Sum the areas of all sections to find the total distance. Total Distance = Area_1 + Area_2 + Area_3 + Area_4 Total Distance = 60 m + 60 m + 90 m + 120 m Total Distance = 330 m The total distance travelled by the object is 330 m.