A motorist drives north for 40.0 min at 90.0 km/h and then stops for 15.0 min. He then continues north, traveling 130 km in 2.00 h.
(a) What is his total displacement?(b) What is his average velocity?
total displacement= 40/60 * 90 + 120*2 N
avg velocity= total dislacement/total time
Total time is 3 hrs.
To find the total displacement, we need to calculate the displacement for each segment of the drive and then add them together.
For the first segment, we can use the formula: displacement = velocity * time.
The motorist drives north for 40.0 min at 90.0 km/h, so the displacement for the first segment is:
displacement1 = (90.0 km/h) * (40.0 min) = (90.0 km/h) * (40.0/60) h = 60.0 km.
For the second segment, the motorist stops for 15.0 min, so there is no displacement.
For the third segment, the motorist drives north and travels 130 km in 2.00 h, so the displacement for the third segment is:
displacement3 = (130 km) - (0 km) = 130 km.
Now, we add up the displacements to get the total displacement:
total displacement = displacement1 + displacement2 + displacement3 = 60.0 km + 0 km + 130 km = 190 km.
Therefore, the total displacement is 190 km.
To find the average velocity, we need to calculate the total displacement and divide it by the total time.
The total time is the sum of the times for each segment: 40.0 min + 15.0 min + 2.00 h = 55 min + 2.00 h.
To convert minutes to hours, we divide by 60:
total time = (55 min + 2.00 h) / 60 = (55/60) h + 2.00 h = 0.92 h + 2.00 h = 2.92 h.
Now, we can calculate the average velocity using the formula: average velocity = total displacement / total time.
average velocity = (190 km) / (2.92 h) ≈ 65.07 km/h.
Therefore, the average velocity is approximately 65.07 km/h.