1. Heather and Matthew walk with an average velocity of 0.98m/s eastward. If it takes them 34 min to walk to the store, what is their displacement? 2. If Joe rides his bicycle in a straight line for 15 min with an average velocity of 12.5km/h south, how far has he ridden? 3. It takes you 95 min to walk with an average velocity of 1.2m/s to the north from the bus stop to the museum entrance. What is your displacement? 4. Simpson drives his car with an average velocity of 48.0km/h to the east. How long will it take him to drive 144 km on a straight highway? 5. Look back at item 4. How much time would Simpson save by increasing his average velocity to 56.0km/h to the east? 6. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then, it travels 210 km south with an average velocity of 75km/h to the south. a. How long does the total trip last? b. What is the average velocity for the total trip?

1. To find the displacement, we can use the formula: displacement = velocity * time. Given that Heather and Matthew walk with an average velocity of 0.98 m/s eastward and it takes them 34 minutes to walk to the store, we can calculate the displacement as follows:<br /><br />Displacement = 0.98 m/s * (34 min * 60 s/min) = 0.98 m/s * 2040 s = 2000.16 m<br /><br />Therefore, their displacement is approximately 2000.16 meters.<br /><br />2. To find the distance Joe has ridden, we can use the formula: distance = velocity * time. Given that Joe rides his bicycle in a straight line for 15 minutes with an average velocity of 12.5 km/h south, we can calculate the distance as follows:<br /><br />Distance = 12.5 km/h * (15 min * 60 s/min) = 12.5 km/h * 900 s = 11250 m<br /><br />Therefore, Joe has ridden a distance of 11250 meters.<br /><br />3. To find the displacement, we can use the formula: displacement = velocity * time. Given that it takes you 95 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance, we can calculate the displacement as follows:<br /><br />Displacement = 1.2 m/s * (95 min * 60 s/min) = 1.2 m/s * 5700 s = 6840 m<br /><br />Therefore, your displacement is approximately 6840 meters.<br /><br />4. To find the time it takes Simpson to drive 144 km on a straight highway with an average velocity of 48.0 km/h to the east, we can use the formula: time = distance / velocity. Given that the distance is 144 km and the average velocity is 48.0 km/h, we can calculate the time as follows:<br /><br />Time = 144 km / 48.0 km/h = 3 hours<br /><br />Therefore, it will take Simpson 3 hours to drive 144 km on a straight highway.<br /><br />5. To find the time Simpson would save by increasing his average velocity to 56.0 km/h to the east, we can use the formula: time = distance / velocity. Given that the distance is 144 km and the new average velocity is 56.0 km/h, we can calculate the new time as follows:<br /><br />New time = 144 km / 56.0 km/h = 2.5714 hours<br /><br />The time saved is the difference between the original time and the new time:<br /><br />Time saved = Original time - New time = 3 hours - 2.5714 hours = 0.4286 hours<br /><br />Therefore, Simpson would save approximately 0.4286 hours (or about 25.7 minutes) by increasing his average velocity to 56.0 km/h to the east.<br /><br />6. a. To find the total time for the trip, we need to add up the time spent traveling and the time spent stopped. Given that the bus travels 280 km south with an average velocity of 88 km/h, it stops for 24 minutes, and then it travels 210 km south with an average velocity of 75 km/h, we can calculate the total time as follows:<br /><br />Time spent traveling = (280 km / 88 km/h) + (210 km / 75 km/h) = 3.18 hours + 2.8 hours = 5.98 hours<br /><br />Time spent stopped = 24 minutes = 0.4 hours<br /><br />Total time = Time spent traveling + Time spent stopped = 5.98 hours + 0.4 hours = 6.38 hours<br /><br />Therefore, the total trip lasts approximately 6.38 hours.<br /><br />b. To find the average velocity for the total trip, we can use the formula: average velocity = total distance / total time. Given that the total distance is 280 km + 210 km = 490 km and the total time is 6.38 hours, we can calculate the average velocity as follows:<br /><br />Average velocity = 490 km / 6.38 hours = 77.17 km/h<br /><br />Therefore, the average velocity for the total trip is approximately 77.17 km/h.