Question 5 [3 marks] Find: (a) the acceleration when t = 4, (b) the total distance travelled, (c) the average speed for the whole journey.

Here's how to solve the problem using the provided velocity-time graph. a) The acceleration when t = 4: Acceleration is the gradient of the velocity-time graph. At t=4 s, the graph is in the first segment, which is a straight line from (0 s, 0 m/s) to (10 s, 15 m/s). Step 1: Identify the coordinates of the segment. The initial point is (t_1, v_1) = (0 s, 0 m/s) and the final point is (t_2, v_2) = (10 s, 15 m/s). Step 2: Calculate the acceleration using the gradient formula. a = ( v)/( t) = (v_2 - v_1)/(t_2 - t_1) = 15 m/s - 0 m/s10 s - 0 s = 15 m/s10 s = 1.5 m/s^2 The acceleration when t=4 s is 1.5 m/s^2. b) The total distance travelled: The total distance travelled is the area under the velocity-time graph. We can divide the graph into three sections: a triangle, a rectangle, and another triangle. Step 1: Calculate the area of the first section (triangle from t=0 to t=10 s). Area_1 = (1)/(2) × base × height = (1)/(2) × 10 s × 15 m/s = 75 m Step 2: Calculate the area of the second section (rectangle from t=10 to t=40 s). Area_2 = width × height = (40 s - 10 s) × 15 m/s = 30 s × 15 m/s = 450 m Step 3: Calculate the area of the third section (triangle from t=40 to t=60 s). Area_3 = (1)/(2) × base × height = (1)/(2) × (60 s - 40 s) × 15 m/s = (1)/(2) × 20 s × 15 m/s = 150 m Step 4: Calculate the total distance by summing the areas. Total Distance = Area_1 + Area_2 + Area_3 = 75 m + 450 m + 150 m = 675 m The total distance travelled is 675 m. c) The average speed for the whole journey: Average speed is the total distance travelled divided by the total time taken. Step 1: Identify the total distance and total time. Total distance = 675 m (from part b) Total time = 60 s (from the graph) Step 2: Calculate the average speed. Average Speed = Total DistanceTotal Time = 675 m60 s = 11.25 m/s The average speed for the whole journey is 11.25 m/s. Last free one today — make it count tomorrow, or type /upgrade for unlimited.