The figure shows a velocity-time graph for a car.

Here's the solution to question 6: The figure shows a velocity-time graph for a car. The graph consists of three parts: 1. Acceleration from t=0 s to t=4 s, reaching a maximum velocity V_m. 2. Constant velocity V_m from t=4 s to t=10 s. 3. Deceleration from t=10 s to t=12 s, coming to rest. The total distance travelled is the area under the velocity-time graph. Step 1: Determine the maximum velocity (V_m). The problem states that the distance travelled in the first four seconds is 32 meters. This corresponds to the area of the triangle from t=0 s to t=4 s. The area of a triangle is given by (1)/(2) × base × height. Distance = (1)/(2) × time × V_m 32 m = (1)/(2) × 4 s × V_m 32 = 2 V_m V_m = (32)/(2) V_m = 16 m/s Step 2: Calculate the total distance travelled for the whole journey. The total distance is the area of the entire trapezium. The area of a trapezium is given by (1)/(2) × (sum of parallel sides) × height. In this graph: • The parallel sides are the time durations at the top and bottom of the trapezium. • The top parallel side (constant velocity duration) is from t=4 s to t=10 s, so its length is 10 - 4 = 6 s. • The bottom parallel side (total time duration) is from t=0 s to t=12 s, so its length is 12 - 0 = 12 s. • The height of the trapezium is the maximum velocity V_m = 16 m/s. Total distance = (1)/(2) × (6 s + 12 s) × 16 m/s Total distance = (1)/(2) × 18 s × 16 m/s Total distance = 9 s × 16 m/s Total distance = 144 m Step 3: Calculate the average velocity for the whole journey. Average velocity is defined as total distance divided by total time. Average velocity = Total distanceTotal time Average velocity = 144 m12 s Average velocity = 12 m/s The average velocity for the whole journey is 12 m/s. 3 done, 2 left today. You're making progress.