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?

1 answer

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.