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
a) i) The speed of the car when t=4 seconds. Step 1: Identify the coordinates on the graph. The graph is a straight line from (0, 20) to (8, 10). To find the speed at t=4, we can find the equation of this line or use similar triangles/interpolation. The slope (acceleration) for 0 t 8 is: a = (10 - 20)/(8 - 0) = (-10)/(8) = -1.25 m/s^2 The equation of the line is v = -1.25t + 20. Step 2: Substitute t=4 into the equation. v = -1.25(4) + 20 v = -5 + 20 v = 15 m/s The speed of the car when t=4 is 15 m/s. ii) The acceleration when t=12 seconds. Step 1: Identify the section of the graph for t=12. For the time interval 8 t 16, the graph is a horizontal line at a constant speed of 10 m/s. Step 2: Calculate the acceleration. Acceleration is the gradient of the speed-time graph. Since the speed is constant, the gradient is zero. a = ( v)/( t) = (10 - 10)/(16 - 8) = (0)/(8) = 0 m/s^2 The acceleration when t=12 is 0 m/s^2. b) Calculate the total distance travelled during the 16 seconds. Step 1: The total distance travelled is the area under the speed-time graph. The area can be divided into two parts: a trapezium from t=0 to t=8 and a rectangle from t=8 to t=16. Step 2: Calculate the area of the trapezium (0 t 8). The parallel sides are v_1 = 20 m/s (at t=0) and v_2 = 10 m/s (at t=8). The height is t = 8 - 0 = 8 s. Area_1 = (1)/(2)(v_1 + v_2) t = (1)/(2)(20 + 10)(8) Area_1 = (1)/(2)(30)(8) = 15 × 8 = 120 m Step 3: Calculate the area of the rectangle (8 t 16). The width is t = 16 - 8 = 8 s. The height (speed) is 10 m/s. Area_2 = width × height = 8 × 10 = 80 m Step 4: Calculate the total distance. Total Distance = Area_1 + Area_2 = 120 m + 80 m = 200 m The total distance travelled during the 16 seconds is 200 m. Drop the next question! 📸