A motorist drives north for 30.0 minutes at 62.0 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?
(b) What is his average velocity?
(a) (42min/hr) x (1hr/60min) = 0.7hr
(76.5km/hr) x 0.7 hr = 53.55 km (Part1)
Part2 - 130 km
Part1+part2=53.55km+130km=183.55km
Same problem different numbers
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 h.
(a) What is his total displacement?
(b) What is his average velocity?
169.58km and 65.72km/hr
To find the total displacement and average velocity of the motorist, we will break down the problem and solve it step by step.
(a) Total Displacement:
Displacement is a vector quantity that represents the change in position from the initial point to the final point. In this case, we need to find the northward displacement.
Step 1: Calculate the displacement during the first leg of the trip.
The motorist drives north for 30.0 minutes at 62.0 km/h. To find the displacement, we need to multiply the speed by the time traveled.
Distance = Speed × Time
Distance = 62.0 km/h × (30.0 min / 60.0 min) [Converting minutes to hours]
Distance = 31.0 km
Since the motorist is driving north, the displacement is also 31.0 km north.
Step 2: Calculate the displacement during the second leg of the trip.
The motorist travels north for 130 km in 1.90 hours. Again, we multiply the speed by the time traveled.
Distance = Speed × Time
Distance = 130 km / 1.90 h
Distance = 68.42 km
Since the motorist is traveling north, the displacement is 68.42 km north.
Step 3: Calculate the total displacement.
To find the total displacement, we simply add the displacements from each leg of the trip.
Total Displacement = Displacement Leg 1 + Displacement Leg 2
Total Displacement = 31.0 km + 68.42 km
Total Displacement = 99.42 km
Therefore, the total displacement of the motorist is 99.42 km north.
(b) Average Velocity:
Average Velocity is defined as the total displacement divided by the total time taken.
Average Velocity = Total Displacement / Total Time Taken
Step 1: Calculate the total time taken.
The motorist drives for 30.0 minutes in the first leg and stops for 15.0 minutes before continuing the journey. So, the total time taken is the sum of both time intervals.
Total Time Taken = 30.0 min + 15.0 min
Total Time Taken = 45.0 min
Step 2: Convert the total time taken to hours.
Since the speed is given in km/h, we need to convert the time from minutes to hours.
Total Time Taken = 45.0 min / 60.0 min/h
Total Time Taken = 0.75 h
Step 3: Calculate the average velocity.
Now, we can divide the total displacement by the total time taken.
Average Velocity = Total Displacement / Total Time Taken
Average Velocity = 99.42 km / 0.75 h
Average Velocity ≈ 132.56 km/h
Therefore, the average velocity of the motorist is approximately 132.56 km/h north.