A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 22 minutes at an average speed of 6.50m/s. During the second part, she rides for 36 minutes at an average speed of 4.30m/s. Finally, during the third part, she rides for 8.0 minutes at an average speed of 13.7m/s. How far has the bicyclist traveled during the entire trip?
b). What is her average velocity for the trip?
Convert min. to seconds:
t1 = 22min * 60s/min = 1320 s.
t2 = 36min * 60s./min = 2160 s.
t3 = 8min * 60s/min = 480 s.
a. D = V1*t1 + V2*t2 + V3*t3.
D = 6.5*1320 + 4.30 * 2160 + 13.7*480 =
24,444 m. = Total dist. traveled.
b. T = t1 + t2 + t3.
T=1320 + 2160 + 480=3960 s.=Tot. time.
Vavg = D/T = 24444m/3960s = 6.17 m/s.
Well, let's calculate the distances for each part of the trip first.
For the first part, the distance can be calculated using the formula d = v * t, where v is the average speed and t is the time. So, for the first part, the distance would be:
d1 = 6.50m/s * 22 minutes
For the second part:
d2 = 4.30m/s * 36 minutes
And for the third part:
d3 = 13.7m/s * 8.0 minutes
Now, to find the total distance, we just add up the distances for each part:
total distance = d1 + d2 + d3
As for the average velocity, well velocity is a vector quantity that takes into account both magnitude and direction. Since the bicyclist traveled only in the north direction, her average velocity will also be in the north direction.
So, her average velocity for the entire trip can be calculated by dividing the total displacement (which is the total distance northward) by the time taken for the entire trip.
Now, let's calculate the total distance and the average velocity without clowning around:
total distance = (6.50m/s * 22 minutes) + (4.30m/s * 36 minutes) + (13.7m/s * 8.0 minutes)
average velocity = total distance / (22 minutes + 36 minutes + 8.0 minutes)
I'll leave the actual calculation to you, but remember to convert the time into a consistent unit (like seconds) before performing the calculations. Good luck!
To find the total distance traveled during the entire trip, we need to calculate the distance traveled during each part and add them together.
Step 1: Calculate the distance traveled during the first part.
Given:
Time = 22 minutes = 22/60 hours
Average speed = 6.50 m/s
Distance = Average speed * Time
Distance = 6.50 m/s * (22/60) hours
Step 2: Calculate the distance traveled during the second part.
Given:
Time = 36 minutes = 36/60 hours
Average speed = 4.30 m/s
Distance = Average speed * Time
Distance = 4.30 m/s * (36/60) hours
Step 3: Calculate the distance traveled during the third part.
Given:
Time = 8.0 minutes = 8.0/60 hours
Average speed = 13.7 m/s
Distance = Average speed * Time
Distance = 13.7 m/s * (8.0/60) hours
Step 4: Add up the distances from all three parts to find the total distance traveled.
Total Distance = Distance of part 1 + Distance of part 2 + Distance of part 3
Now, let's calculate the distances and then sum them up:
Distance of part 1 = 6.50 * (22/60)
Distance of part 2 = 4.30 * (36/60)
Distance of part 3 = 13.7 * (8.0/60)
Total Distance = (6.50 * (22/60)) + (4.30 * (36/60)) + (13.7 * (8.0/60))
Now, let's calculate the total distance.
To find the distance traveled during the entire trip, we need to calculate the distance traveled during each part and then sum them up.
The distance traveled during each part can be found by multiplying the average speed by the time traveled:
1. Distance for the first part = (average speed of 6.50 m/s) x (22 minutes). To calculate this, first convert the time from minutes to seconds by multiplying by 60: 22 minutes x 60 seconds/minute = 1320 seconds.
Distance for the first part = (6.50 m/s) x (1320 seconds).
2. Distance for the second part = (average speed of 4.30 m/s) x (36 minutes). Convert the time to seconds: 36 minutes x 60 seconds/minute = 2160 seconds.
Distance for the second part = (4.30 m/s) x (2160 seconds).
3. Distance for the third part = (average speed of 13.7 m/s) x (8 minutes). Convert the time to seconds: 8 minutes x 60 seconds/minute = 480 seconds.
Distance for the third part = (13.7 m/s) x (480 seconds).
Now, we can calculate the total distance traveled during the entire trip by summing up the distances from each part:
Total distance = Distance for the first part + Distance for the second part + Distance for the third part.
To find the average velocity for the trip, we need to divide the total displacement by the total time taken:
Average velocity = Total displacement / Total time taken.
Since the bicyclist traveled in the same direction, we can use displacement instead of distance for the average velocity calculation.
Now, you can calculate the distance traveled during the entire trip and the average velocity using the given information.