The displacement-time graph shows a person walking along a road. A) Calculate the average velocity of the whole journey. B) Calculate the instantaneous velocity at point B. C) Calculate the average velocity fro t = 7 to t = 15 seconds.

Here are the solutions to the displacement-time graph questions:

A) Calculate the average velocity of the whole journey. Average velocity is defined as the total displacement divided by the total time taken. Step 1: Identify the initial and final displacement and time from the graph. • Initial displacement at $t=0 \text{ s}$ is $0 \text{ m}$. • Final displacement at $t=20 \text{ s}$ is $0 \text{ m}$. • Total time is $20 \text{ s}$. Step 2: Calculate the total displacement and average velocity. $Total Displacement = Final Displacement - Initial Displacement = 0 m - 0 m = 0 m$ $Average Velocity = \frac{Total Displacement}{Total Time} = \frac{0 m}{20 s} = 0 m/s$ The average velocity of the whole journey is $\boxed{0 m/s}$.

B) Calculate the instantaneous velocity at point B. Instantaneous velocity on a displacement-time graph is the gradient (slope) of the graph at that specific point. Point B is located at $(16 s, -20 m)$. This point lies on the straight line segment from $t=14 \text{ s}$ to $t=20 \text{ s}$. Step 1: Identify two points on the straight line segment that includes point B. • Point 1: $(t_1, d_1) = (14 s, -30 m)$ • Point 2: $(t_2, d_2) = (20 s, 0 m)$ Step 2: Calculate the gradient (velocity) using these two points. $Velocity = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1} = \frac{0 m - (-30 m)}{20 s - 14 s} = \frac{30 m}{6 s} = 5 m/s$ The instantaneous velocity at point B is $\boxed{5 m/s}$.

C) Calculate the average velocity from $t=7 \text{ s}$ to $t=15 \text{ s}$. Average velocity is the total displacement over the given time interval. Step 1: Find the displacement at $t=7 \text{ s}$ and $t=15 \text{ s}$ from the graph. • At $t=7 \text{ s}$, the displacement is $20 \text{ m}$. • At $t=15 \text{ s}$, the point is on the segment from $(14 s, -30 m)$ to $(20 s, 0 m)$. The velocity of this segment is $5 \text{ m/s}$ (from part B). Displacement at $t=15 s = Displacement at t=14 s + (velocity \times \Delta t)$ $d_{15s} = -30 m + (5 m/s \times (15 s - 14 s)) = -30 m + (5 m/s \times 1 s) = -30 m + 5 m = -25 m$ Step 2: Calculate the total displacement and average velocity for the interval. $Total Displacement = d_{15s} - d_{7s} = -25 m - 20 m = -45 m$ $Total Time = 15 s - 7 s = 8 s$ $Average Velocity = \frac{Total Displacement}{Total Time} = \frac{-45 m}{8 s} = -5.625 m/s$ The average velocity from $t=7 \text{ s}$ to $t=15 \text{ s}$ is $\boxed{-5.625 m/s}$.