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
1) Calculate the acceleration of the particle in the first 10 seconds. Step 1: Identify the initial and final velocities and the time interval from the graph. From t=0 s to t=10 s: Initial velocity, u = 30 m/s Final velocity, v = 10 m/s Time interval, t = 10 s Step 2: Use the formula for acceleration. Acceleration a = (v - u)/( t) a = 10 m/s - 30 m/s10 s a = -20 m/s10 s a = -2 m/s^2 The acceleration of the particle in the first 10 seconds is -2 m/s^2. 2) The value of t if it travelled 50 meters from 20th seconds. Step 1: Identify the shape and dimensions of the graph segment from t=20 s to t=t s. This segment is a triangle. Initial velocity at t=20 s is 10 m/s. Final velocity at t=t s is 0 m/s. The base of the triangle is (t - 20) s. The height of the triangle is 10 m/s. The distance travelled is the area under this segment, which is given as 50 m. Step 2: Set up the equation for the area of the triangle and solve for t. Area of triangle = (1)/(2) × base × height 50 m = (1)/(2) × (t - 20) s × 10 m/s 50 = 5 × (t - 20) Divide both sides by 5: 10 = t - 20 Add 20 to both sides: t = 10 + 20 t = 30 s The value of t is 30 s. 3) The average speed for the whole journey. Step 1: Calculate the total distance travelled. This is the total area under the graph from t=0 s to t=30 s. The journey consists of three parts: • Part 1 (0 to 10 s): A trapezium. Area_1 = (1)/(2) × (sum of parallel sides) × height Area_1 = (1)/(2) × (30 m/s + 10 m/s) × 10 s Area_1 = (1)/(2) × 40 m/s × 10 s = 200 m • Part 2 (10 to 20 s): A rectangle. Area_2 = length × width Area_2 = 10 m/s × (20 - 10) s = 10 m/s × 10 s = 100 m • Part 3 (20 to 30 s): A triangle. The distance for this part is given as 50 m in question 2. Area_3 = 50 m Total distance = Area_1 + Area_2 + Area_3 Total distance = 200 m + 100 m + 50 m = 350 m Step 2: Determine the total time taken for the journey. Total time = t = 30 s (from question 2). Step 3: Calculate the average speed. Average speed = Total distance travelledTotal time taken Average speed = 350 m30 s Average speed = (35)/(3) m/s Average speed ≈ 11.67 m/s The average speed for the whole journey is 11.67 m/s. Drop the next question.