Can you give me that answer in english

Based on the given graph, we will solve each part:

Key points from the graph:

• At $t=0$, $x=6$
• At $t=4$, $x=3$
• At $t=7$, $x=3$
• At $t=9$, $x=0$
• At $t=11$, $x=3$
• At $t=12.5$, $x=0$

i) Distance from $t=0$ to $t=11$
Distance is the total length of the path traveled.

• From $t=0$ to $t=4$: Position changes from 6 to 3. Distance $= |3-6| = 3$ units.
• From $t=4$ to $t=7$: Position remains constant at 3. Distance $= |3-3| = 0$ units.
• From $t=7$ to $t=9$: Position changes from 3 to 0. Distance $= |0-3| = 3$ units.
• From $t=9$ to $t=11$: Position changes from 0 to 3. Distance $= |3-0| = 3$ units.

Total distance $= 3 + 0 + 3 + 3 = 9$ units.

$$\boxed{\text{9 units}}$$

ii) Displacement from $t=5$ to $t=12.5$
Displacement is the difference between the final and initial positions.

• Initial position at $t=5$: From the graph, the position is $x=3$ from $t=4$ to $t=7$. So, $x(5) = 3$ units.
• Final position at $t=12.5$: From the graph, $x(12.5) = 0$ units.

Displacement $= x(12.5) - x(5) = 0 - 3 = -3$ units.

$$\boxed{\text{-3 units}}$$

iii) Average speed from $t=0$ to $t=9$
Average speed = Total distance / Total time.

• Total time from $t=0$ to $t=9$ is $9 - 0 = 9$ s.
• Total distance from $t=0$ to $t=9$:
  • From $t=0$ to $t=4$: Distance $= 3$ units.
  • From $t=4$ to $t=7$: Distance $= 0$ units.
  • From $t=7$ to $t=9$: Distance $= 3$ units. Total distance $= 3 + 0 + 3 = 6$ units.

Average speed $= \frac{6}{9} = \frac{2}{3}$ units/s.

$$\boxed{\frac{2}{3} \text{ units/s}}$$

iv) Average velocity from $t=7$ to $t=12$
Average velocity = Total displacement / Total time.

• Total time from $t=7$ to $t=12$ is $12 - 7 = 5$ s.

• Initial position at $t=7$: $x(7) = 3$ units.

• To find the final position at $t=12$: From $t=11$ to $t=12.5$, the graph is a straight line from $(11, 3)$ to $(12.5, 0)$. The slope of this line $m = \frac{0-3}{12.5-11} = \frac{-3}{1.5} = -2$. Using the equation of a line $x - x_1 = m(t - t_1)$: $x - 3 = -2(t - 11)$ $x = -2t + 22 + 3$ $x = -2t + 25$ At $t=12$, $x(12) = -2(12) + 25 = -24 + 25 = 1$ unit.

• Displacement $= x(12) - x(7) = 1 - 3 = -2$ units.

Average velocity $= \frac{-2}{5} = -0.4$ units/s.

$$\boxed{\text{-0.4 units/s}}$$