A commuting student leaves home and drives to school at an average speed of 42.0 km/h. After 20.0 min he realizes that he has forgotten his homework and returns home to get it at the same average speed. It takes 7.0 min to find the report, after which the trip to school 42.0 km away to the east is resumed at the same speed as before.
What is the average speed for the entire trip ?
What is the average velocity for the entire trip?
a. d1=42km/h*(40/60)h =28 km.
t1 = 28/42+7/60 = 0.783 h
d2 = 42km to school.
t2 = d2/r = 42km/42km/h = 1 h.
D = d1 + d2 = 28 + 42 = 70 km = Total driving distance.
Speed=D/(t1+t2)=70/(0.783+1)=39.25 km/h
Well, it seems like this student has a case of forgetfulness! Let's crunch some numbers to help them out.
To find the average speed for the entire trip, we need to first calculate the total travel time. The student spends 20 minutes driving back home plus 7 minutes searching for the report, which gives us a total of 27 minutes or 0.45 hours.
Now let's calculate the distance traveled. The student drives to school (42 km) and then drives back home again (42 km). So the total distance traveled is 84 km.
To find the average speed, we divide the total distance by the total time: 84 km ÷ 0.45 hours = 186.67 km/h (approximately).
Now, let's move on to average velocity. Velocity is a vector quantity, which means it includes both magnitude and direction. Here, the student drives to school and then drives back home, so the displacement is zero. Therefore, the average velocity for the entire trip is zero.
So, to sum it up:
Average speed: Approximately 186.67 km/h
Average velocity: Zero (the student ends up back where they started, so no overall displacement)
Remember, kids, always double-check for homework before you leave home, unless you want to take an entertaining round trip like this student!
To find the average speed for the entire trip, we need to calculate the total distance traveled divided by the total time taken.
Step 1: Calculate the total distance traveled.
- Distance from home to school (one way): 42.0 km
- Distance traveled while returning home: 42.0 km
Total distance = Distance one way + Distance returning home
Total distance = 42.0 km + 42.0 km = 84.0 km
Step 2: Calculate the total time taken.
- Time taken to drive to school: 20.0 min
- Time taken to return home: 7.0 min
- Time taken to drive back to school: 0 min (since he resumed the trip right after finding the report)
Total time = Time to school + Time returning home + Time back to school
Total time = 20.0 min + 7.0 min + 0 min = 27.0 min
Step 3: Convert total time to hours.
Since we want to find the average speed in km/h, we need the total time in hours.
27.0 min is equivalent to 27.0/60 = 0.45 hours.
Step 4: Calculate average speed.
Average speed = Total distance / Total time
Average speed = 84.0 km / 0.45 hours
Average speed = 186.7 km/h (rounded to one decimal place)
Therefore, the average speed for the entire trip is approximately 186.7 km/h.
To find the average velocity, we need to consider the direction of motion.
Step 1: Determine the direction of motion.
The student initially drove to the east from home to school and returned in the same direction.
Step 2: Calculate the total displacement.
The total displacement is the difference in position between the starting point (home) and the ending point (school).
Since the student returned to the same position after going home and finding the report, the total displacement is zero.
Step 3: Calculate the total time taken.
We calculated the total time taken as 27.0 min in the previous calculation.
Step 4: Convert total time to hours.
27.0 min is equivalent to 27.0/60 = 0.45 hours.
Step 5: Calculate average velocity.
Average velocity = Total displacement / Total time
Average velocity = 0 km / 0.45 hours
Average velocity = 0 km/h
Therefore, the average velocity for the entire trip is 0 km/h, as there was no net displacement in any direction.
To find the average speed for the entire trip, we need to first find the total distance traveled and the total time taken.
First, let's find the total distance traveled.
The student drove to school, then returned home, and then drove to school again. So, the total distance traveled is the distance from home to school and back to home, plus the distance from home to school again.
Given that the distance from home to school is 42.0 km, the total distance traveled is:
Total distance = 2(distance from home to school) + distance from home to school = 2(42.0 km) + 42.0 km = 126.0 km
Next, let's find the total time taken.
The student drove to school for 20.0 min, then returned home for 7.0 min, and then drove to school again. So, the total time taken is the time taken to drive to school, plus the time taken to return home, plus the time taken to drive back to school.
Given that the average speed during each leg of the trip is 42.0 km/h, we can calculate the total time taken as follows:
Total time = (Time taken to drive to school) + (Time taken to return home) + (Time taken to drive back to school) = (20.0 min) + (7.0 min) + (20.0 min) = 47.0 min
Now, let's convert the total time to hours:
Total time = 47.0 min ÷ 60 min/hour = 0.783 hours
Finally, to find the average speed for the entire trip, we divide the total distance traveled by the total time taken:
Average speed = Total distance ÷ Total time = 126.0 km ÷ 0.783 hours
Using a calculator, we find that the average speed for the entire trip is approximately 160.94 km/h.
To find the average velocity for the entire trip, we need to consider both the magnitude and the direction of the displacements during each leg of the trip.
Since the student drives to school and back along the same route, the total displacement is zero. The average velocity will also be zero as displacement is a vector quantity and the magnitude is zero.