2.2. A motorist drives north for 45.0 minutes at $$ 105.0 \mathrm{~km} / \mathrm{h} $$ and then stop for 22.0 minutes. He next continues north, travelling 130 km in 90 minutes. $$ \begin{array}{ll} ext { (a) What is his total displacement? } \ ext { (b) What is his average velocity? }\end{array} $$

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2.2. A motorist drives north for 45.0 minutes at $$ 105.0 \mathrm{~km} / \mathrm{h} $$ and then stop for 22.0 minutes. He next continues north, travelling 130 km in 90 minutes. $$ \begin{array}{ll}	ext { (a) What is his total displacement? } \ 	ext { (b) What is his average velocity? }\end{array} $$

UpStudy AI · Accepted Answer

1. **Convert the time intervals to hours:**

- **First segment:**  
     $$
     45.0\text{ minutes} = \frac{45.0}{60} = 0.75\text{ hours}
     $$
     
   - **Stop:**  
     $$
     22.0\text{ minutes} = \frac{22.0}{60} \approx 0.3667\text{ hours}
     $$
     
   - **Third segment:**  
     $$
     90\text{ minutes} = \frac{90}{60} = 1.5\text{ hours}
     $$

2. **Calculate the displacement for each moving segment:**

- **First segment (northward):**  
     $$
     \text{Distance}_1 = 105.0\,\frac{\text{km}}{\text{h}} \times 0.75\text{ h} = 78.75\text{ km}
     $$
     
   - **Stop:** There is no displacement during the stop.

- **Third segment (northward):**  
     The distance is given directly as 130 km.

3. **Determine the total displacement:**

Since the motorist only travels north, the total displacement is the sum of the distances from the moving segments.
   
   $$
   \text{Total displacement} = 78.75\text{ km} + 130\text{ km} = 208.75\text{ km (north)}
   $$

4. **Compute the total time elapsed:**

$$
   \text{Total time} = 0.75\text{ h} + 0.3667\text{ h} + 1.5\text{ h} = 2.6167\text{ h}
   $$

5. **Calculate the average velocity:**

The average velocity is given by the total displacement divided by the total time.
   
   $$
   \text{Average velocity} = \frac{208.75\text{ km}}{2.6167\text{ h}} \approx 79.75\,\frac{\text{km}}{\text{h}} \text{ (north)}
   $$

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**Answers:**

(a) $$208.75\,\text{km}$$ (north)

(b) $$79.75\,\frac{\text{km}}{\text{h}}$$ (north)
(a) Total displacement is 208.75 km north. (b) Average velocity is 79.75 km/h north.

2.2. A motorist drives north for 45.0 minutes at and then stop for 22.0 minutes. He next
continues north, travelling 130 km in 90 minutes.

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2.2. A motorist drives north for 45.0 minutes at and then stop for 22.0 minutes. He next continues north, travelling 130 km in 90 minutes.