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!

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.