Consider the the table below indicating the position of the car at various time. Find displacement, average velocity and average speed.

The table provides the position ($x$) of the car at various times ($t$). We need the values for points A and F, and all intermediate points to calculate total distance.

• Point A: $t_A = 0 \text{ s}$, $x_A = 0 \text{ m}$
• Point B: $t_B = 1 \text{ s}$, $x_B = 12 \text{ m}$
• Point C: $t_C = 2 \text{ s}$, $x_C = 24 \text{ m}$
• Point D: $t_D = 3 \text{ s}$, $x_D = 20 \text{ m}$
• Point E: $t_E = 4 \text{ s}$, $x_E = 12 \text{ m}$
• Point F: $t_F = 5 \text{ s}$, $x_F = 20 \text{ m}$

Displacement ($\Delta x$) is the change in position from the initial point (A) to the final point (F).

$$\Delta x = x_F - x_A$$ $$\Delta x = 20 \text{ m} - 0 \text{ m}$$ $$\Delta x = \boxed{20 \text{ m}}$$

Average velocity ($\bar{v}$) is the displacement divided by the total time taken.
The total time taken is $\Delta t = t_F - t_A = 5 \text{ s} - 0 \text{ s} = 5 \text{ s}$.

$$\bar{v} = \frac{\Delta x}{\Delta t}$$ $$\bar{v} = \frac{20 \text{ m}}{5 \text{ s}}$$ $$\bar{v} = \boxed{4 \text{ m/s}}$$

Distance is the sum of the absolute changes in position between consecutive points.

• Distance A to B: $|x_B - x_A| = |12 \text{ m} - 0 \text{ m}| = 12 \text{ m}$
• Distance B to C: $|x_C - x_B| = |24 \text{ m} - 12 \text{ m}| = 12 \text{ m}$
• Distance C to D: $|x_D - x_C| = |20 \text{ m} - 24 \text{ m}| = |-4 \text{ m}| = 4 \text{ m}$
• Distance D to E: $|x_E - x_D| = |12 \text{ m} - 20 \text{ m}| = |-8 \text{ m}| = 8 \text{ m}$
• Distance E to F: $|x_F - x_E| = |20 \text{ m} - 12 \text{ m}| = 8 \text{ m}$ Total distance $d = 12 \text{ m} + 12 \text{ m} + 4 \text{ m} + 8 \text{ m} + 8 \text{ m} = 44 \text{ m}$.

Average speed ($\bar{s}$) is the total distance traveled divided by the total time taken.

$$\bar{s} = \frac{d}{\Delta t}$$ $$\bar{s} = \frac{44 \text{ m}}{5 \text{ s}}$$ $$\bar{s} = \boxed{8.8 \text{ m/s}}$$