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I can help with solving the questions based on the motion graph in the image. Let's break down each question, using the graph data for accurate answers:

1. **What is the object's velocity at 20 s?**
   - At \( t = 20 \) s, the object has a displacement of approximately \( +20 \, \text{m} \).
   - From \( t = 0 \) to \( t = 20 \, \text{s} \), the object moves from \( 0 \, \text{m} \) to \( 20 \, \text{m} \), which is a linear increase. The slope of the line represents the velocity.
   - The slope (velocity) can be calculated as: 
     \[
     v = \frac{\Delta \text{displacement}}{\Delta \text{time}} = \frac{20 \, \text{m} - 0 \, \text{m}}{20 \, \text{s} - 0 \, \text{s}} = \frac{20}{20} = 1 \, \text{m/s}.
     \]
   So, the velocity at \( 20 \, \text{s} \) is \( 1 \, \text{m/s} \).

2. **What is the object's speed at 45 s?**
   - At \( t = 45 \, \text{s} \), the displacement is approximately \( -20 \, \text{m} \).
   - From \( t = 35 \, \text{s} \) to \( t = 45 \, \text{s} \), the object moves from \( +20 \, \text{m} \) to \( -20 \, \text{m} \), indicating a negative slope (negative velocity).
   - The slope (velocity) between \( 35 \, \text{s} \) and \( 45 \, \text{s} \) can be calculated as:
     \[
     v = \frac{-20 \, \text{m} - 20 \, \text{m}}{45 \, \text{s} - 35 \, \text{s}} = \frac{-40}{10} = -4 \, \text{m/s}.
     \]
   Speed is the magnitude of velocity, so the speed at \( 45 \, \text{s} \) is \( 4 \, \text{m/s} \).

3. **What is the object's velocity at 65 s?**
   - At \( t = 65 \, \text{s} \), the object has reached a constant displacement of \( -40 \, \text{m} \), and the graph shows a horizontal line between \( 60 \, \text{s} \) and \( 70 \, \text{s} \), indicating no change in displacement.
   - The velocity during this period is \( 0 \, \text{m/s} \).

4. **How far did the object travel in the first 50 s?**
   - From \( t = 0 \, \text{s} \) to \( t = 50 \, \text{s} \), the object first moves to \( +20 \, \text{m} \) by \( t = 30 \, \text{s} \), and then back to \( 0 \, \text{m} \) by \( t = 50 \, \text{s} \).
   - Total distance traveled is:
     - \( 20 \, \text{m} \) to the right, and then
     - \( 20 \, \text{m} \) back to the origin.
   - Total distance = \( 20 + 20 = 40 \, \text{m} \).

5. **What was the object's displacement at 60 s?**
   - At \( t = 60 \, \text{s} \), the object’s displacement is \( -40 \, \text{m} \).

Would you like more details on any of these calculations?

Here are 5 related questions for further exploration:
1. What is the total displacement after 70 seconds?
2. Calculate the acceleration during the interval from 35 s to 45 s.
3. How long did the object remain at rest during the motion?
4. What is the average velocity over the entire motion from 0 to 70 s?
5. Can you describe the object’s motion in terms of uniform and non-uniform velocity?

**Tip**: Remember that velocity is a vector quantity (it has direction), while speed is scalar (magnitude only).

What is the object's velocity at 20 s? What is the object's speed at 45 s? What is the object's velocity at 65 s? How far did the object travel in the first 50 s? What was the object's displacement at 60 s?

Learn how to determine an object's velocity at different times, calculate speed, and find displacement using a motion graph. Includes step-by-step solutions for questions such as velocity at 20s, speed at 45s, and total distance traveled.

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