A motorist drives north for 37.0 minutes at 87.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in 1.90 h.
(a) What is his total displacement?
km
(b) What is his average velocity?
km/h
To find the total displacement, we need to consider both the distance traveled in the north direction and the distance traveled in the south direction.
First, let's find the northward distance:
Distance = Speed x Time
Distance = 87.0 km/h x (37.0 minutes / 60 minutes) (convert minutes to hours)
Distance = 87.0 km/h x 0.617 h
Distance = 53.8 km (rounded to one decimal place)
Next, let's find the southward distance:
Distance = Speed x Time
Distance = 130 km / 1.90 h
Distance = 68.4 km (rounded to one decimal place)
To find the total displacement, we subtract the southward distance from the northward distance:
Total Displacement = Northward Distance - Southward Distance
Total Displacement = 53.8 km - 68.4 km
Total Displacement = -14.6 km (rounded to one decimal place)
(a) The motorist's total displacement is -14.6 km.
To find the average velocity, we need to consider both the magnitude and direction of the displacement:
Average Velocity = Total Displacement / Total Time
Total Time = Northward Time + Stopping Time + Southward Time
Northward Time = 37.0 minutes / 60 minutes (convert minutes to hours)
Stopping Time = 15.0 minutes / 60 minutes (convert minutes to hours)
Southward Time = 1.90 h
Total Time = (37.0 minutes / 60 minutes) + (15.0 minutes / 60 minutes) + 1.90 h
Total Time = 0.617 h + 0.250 h + 1.90 h
Total Time = 2.767 h (rounded to three decimal places)
Now we can calculate the average velocity:
Average Velocity = (-14.6 km) / (2.767 h)
Average Velocity = -5.276 km/h (rounded to three decimal places)
(b) The motorist's average velocity is -5.276 km/h.