https://file.aiquickdraw.com/mathbot/file/1729267737954wrz72d7o.jpg

Let's analyze the velocity-time graph and solve the questions provided.

### 1. **What is the initial velocity of the object?**
Since the object starts from rest, the initial velocity is **0 m/s** (at time = 0).

### 2. **What is the final velocity of the object?**
The final velocity occurs at point K on the graph, which corresponds to **63.5 seconds**. The velocity at K is **0 m/s**, as the object comes to rest.

### 3. **Determine the acceleration during H to J.**
- At H, time is 46.5 s, and velocity is 0 m/s.
- At J, time is 55.75 s, and velocity is 37 m/s.
  
Using the formula for acceleration:
\[
a = \frac{{v_J - v_H}}{{t_J - t_H}} = \frac{{37 - 0}}{{55.75 - 46.5}} = \frac{37}{9.25} \approx 4.00 \, \text{m/s}^2
\]

### 4. **What time does the object reach its maximum velocity?**
The maximum velocity on the graph is at point B, where the velocity is **31 m/s**. This happens at time **14.5 seconds** (P).

### 5. **Calculate the displacement from E to F.**
The displacement can be calculated from the area under the graph between points E and F. The graph from E to F forms a horizontal line, meaning the object moves with constant velocity:
- Velocity at E and F is 14.75 m/s.
- Time between E (25 s) and F (37 s) is \( 37 - 25 = 12 \, \text{s} \).

Displacement:
\[
\text{Displacement} = \text{velocity} \times \text{time} = 14.75 \times 12 = 177 \, \text{m}
\]

Let me know if you'd like further details or clarifications!

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Here are 5 follow-up questions to explore further:
1. What is the displacement from point B to point D?
2. How would you calculate the average velocity over the entire journey?
3. Can you determine the total displacement of the object from 0 to K?
4. What would the graph look like if the object experienced a deceleration from point B to C?
5. How can we find the acceleration between point G and H?

**Tip:** When calculating displacement from a velocity-time graph, always look at the area under the curve for each segment of motion.

The velocity-time graph of moving object starting from rest is given, where 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. What is the initial velocity of the object? What is the final velocity of the object? Determine acceleration during H to J. What time does the object reach its maximum velocity? Calculate the displacement from E to F. Calculate the displacement from point J to K. Calculate the acceleration from point G to H. What is the acceleration of the object from point D to E? Write the total time in the journey the body does not move.

Solve a detailed physics problem on interpreting a velocity-time graph, including calculations for acceleration, displacement, and the time intervals when the object does not move. This problem is suitable for students in Grades 9-12 and covers core concepts in kinematics and graph analysis.

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