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 $\frac{1}{2} \times \text{base} \times \text{height}$. $$ \text{Distance} = \frac{1}{2} \times \text{time} \times V_m $$ $$ 32 \text{ m} = \frac{1}{2} \times 4 \text{ s} \times V_m $$ $$ 32 = 2 V_m $$ $$ V_m = \frac{32}{2} $$ $$ V_m = 16 \text{ m/s} $$ 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 $\frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$. 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. $$ \text{Total distance} = \frac{1}{2} \times (6 \text{ s} + 12 \text{ s}) \times 16 \text{ m/s} $$ $$ \text{Total distance} = \frac{1}{2} \times 18 \text{ s} \times 16 \text{ m/s} $$ $$ \text{Total distance} = 9 \text{ s} \times 16 \text{ m/s} $$ $$ \text{Total distance} = 144 \text{ m} $$ Step 3: Calculate the average velocity for the whole journey. Average velocity is defined as total distance divided by total time. $$ \text{Average velocity} = \frac{\text{Total distance}}{\text{Total time}} $$ $$ \text{Average velocity} = \frac{144 \text{ m}}{12 \text{ s}} $$ $$ \text{Average velocity} = 12 \text{ m/s} $$ The average velocity for the whole journey is $\boxed{\text{12 m/s}}$. 3 done, 2 left today. You're making progress.