A motorist drives north for 40.0 minutes at 61.5 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in 1.70 h.
(a) What is his total displacement?
(b) What is his average velocity?
To find the total displacement in this scenario, we need to calculate the sum of the individual displacements for each leg of the trip.
(a) Displacement is a vector quantity that represents the change in position of an object. In this case, we can break down the problem into two parts: the first part where the motorist drives for 40.0 minutes at 61.5 km/h, and the second part where the motorist continues driving for 1.70 hours traveling 130 km.
First, let's calculate the displacement for the first part of the trip.
Displacement1 = (time1) x (velocity1)
Given:
time1 = 40.0 minutes = 40.0/60 hours = 0.667 hours
velocity1 = 61.5 km/h
Displacement1 = 0.667 hours x 61.5 km/h
Now, let's calculate the displacement for the second part of the trip.
Displacement2 = (time2) x (velocity2)
Given:
time2 = 1.70 hours
velocity2 = 130 km/1.70 h
Displacement2 = 1.70 hours x (130 km/1.70 hours)
Finally, calculate the total displacement by summing the individual displacements.
Total Displacement = Displacement1 + Displacement2
(b) To find the average velocity, we need to divide the total displacement by the total time taken.
Average Velocity = Total Displacement / Total Time
Given that the motorist stops for 15.0 minutes (0.25 hours) during the trip, we can calculate the total time as:
Total Time = time1 + time2 + stop time
So, total time = 0.667 hours + 1.70 hours + 0.25 hours
Now we have all the necessary values to calculate the average velocity.
I'll calculate the results.
Note: Please wait a moment while I perform the calculations.