Let's analyze this velocity-time graph and address the questions. Here's how we will proceed:

Given Data:

• The graph shows the velocity of an object at different times.
• Specific points and their times (in seconds):
  • $B = 31$
  • $P = 14.5$
  • $C = -26$
  • $D = 8$
  • $E = 14.75$
  • $F = 25$
  • $G = 37$
  • $H = 46.5$
  • $J = 55.75$
  • $K = 63.5$

Approach:

We'll answer each question by interpreting the graph and using physics concepts like:

• The slope of the velocity-time graph represents acceleration.
• The area under the velocity-time graph gives displacement.
• Zero velocity indicates periods where the object is stationary.

Let's solve each question:

1. Initial velocity of the object:

   • The object starts from rest, so at time $D$ (8 seconds), velocity = 0.

2. Final velocity of the object:

   • The final point is $K$ at 63.5 seconds, where the velocity is 0 (since it lies on the time axis).

3. Determine acceleration during $H$ to $J$:

   • Acceleration = (Change in velocity) / (Time interval)
   • From $H$ (velocity is negative) to $J$ (velocity is 0):
     • Change in velocity = $0 - (-26) = 26$ m/s.
     • Time interval = $55.75 - 46.5 = 9.25$ s.
     • Acceleration = $26 / 9.25 \approx 2.81$ m/s².

4. Time when the object reaches its maximum velocity:

   • Maximum positive velocity occurs at point $B$, which is at time $31$ seconds.

5. Calculate displacement from $E$ to $F$:

   • Displacement = Area under the graph from $E$ to $F$.
   • This is a rectangle from $E$ to $F$:
     • Velocity = 14.75 m/s.
     • Time interval = $25 - 14.75 = 10.25$ s.
     • Displacement = $14.75 \times 10.25 \approx 151.19$ m.

Let's continue solving the remaining questions. Let me know if you want detailed explanations for each. Here are some additional questions related to this graph:

1. How do you calculate displacement from other sections of the graph?
2. What is the significance of negative velocity in this context?
3. How is acceleration determined from a negative velocity to zero?
4. What happens when velocity remains constant over a time interval?
5. How can you find the total displacement over the entire journey?

Tip: Always remember that the area under a velocity-time graph represents the displacement of the object. Positive areas indicate forward movement, while negative areas indicate backward movement.