A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north traveling 130 km in 2.00 h. What is his total displacement? What is his average velocity?
To solve this problem, we can break it down into three parts:
Part 1: The motorist drives north for 35.0 minutes at 85.0 km/h.
The distance covered in this part can be calculated using the formula:
Distance = speed × time
= 85.0 km/h × (35.0 minutes / 60.0 minutes per hour)
= 85.0 km/h × 0.583 hours
= 49.455 km
Since the motorist is driving north, the displacement in this part is also 49.455 km north.
Part 2: The motorist stops for 15.0 minutes. During this time, there is no displacement because he is not moving.
Part 3: The motorist continues north and travels 130 km in 2.00 hours.
The displacement in this part is also 130 km north.
Now, let's calculate the total displacement:
Total displacement = Displacement in Part 1 + Displacement in Part 2 + Displacement in Part 3
= 49.455 km + 0 km + 130 km
= 179.455 km
The total displacement is 179.455 km.
To calculate the average velocity, we use the formula:
Average velocity = Total displacement / Total time
The total time is the sum of the times in all three parts:
Total time = Time in Part 1 + Time in Part 2 + Time in Part 3
= 35.0 minutes + 15.0 minutes + 2.00 hours
= 35.0 minutes + 15.0 minutes + 120 minutes
= 170 minutes
Converting the total time to hours:
Total time = 170 minutes / 60.0 minutes per hour
= 2.833 hours
Now we can calculate the average velocity:
Average velocity = Total displacement / Total time
= 179.455 km / 2.833 hours
= 63.296 km/h
The average velocity is 63.296 km/h.