A car makes a 60-km trip with an average velocity of 38.5-km/h in a direction due north. The trip consists of three parts. The car moves with a constant velocity of 25 km/h due north for the first 15 km and 62 km/h due north for the next 32 km. With what constant velocity does the car travel for the last 13-km segment of the trip?
average velocity= total distance/total time
Time for first leg: 15/25 hr
Time for second leg: 32/62
Time for third leg...
total time=60/38.5=you do it.
time for third leg= distance/timethird=
= 13/(totaltime-15/25 - 32/62)
velocity on third leg= 13/time for third
To find the constant velocity of the car for the last 13 km segment of the trip, we need to first calculate the total time it took to travel the entire trip and the total distance covered.
For the first segment, the car traveled at a constant velocity of 25 km/h for 15 km. Therefore, the time taken for this segment is given by:
Time taken for first segment = Distance / Velocity
= 15 km / 25 km/h
= 0.6 hours
For the second segment, the car traveled at a constant velocity of 62 km/h for 32 km. Similarly, we can calculate the time taken for this segment:
Time taken for second segment = Distance / Velocity
= 32 km / 62 km/h
= 0.5161 hours
To find the total time taken for the trip, we add the times taken for each segment:
Total time taken = Time taken for first segment + Time taken for second segment
= 0.6 hours + 0.5161 hours
= 1.1161 hours
Next, we calculate the total distance covered during the trip:
Total distance = Distance of first segment + Distance of second segment + Distance of third segment
= 15 km + 32 km + 13 km
= 60 km
Now, we can find the average velocity for the entire trip by dividing the total distance covered by the total time taken:
Average velocity = Total distance / Total time taken
= 60 km / 1.1161 hours
≈ 53.8 km/h
Since the average velocity is the total displacement divided by the total time taken, we can conclude that the car traveled with an average velocity of approximately 53.8 km/h in a direction due north for the last 13 km segment of the trip.
To find the constant velocity of the car during the last 13-km segment of the trip, we can use the concept of average velocity.
Average velocity is defined as the total displacement divided by the total time taken.
First, let's calculate the total displacement of the car during the trip:
- For the first 15 km segment, the car moves with a constant velocity of 25 km/h due north. So the displacement is 15 km due north.
- For the next 32 km segment, the car moves with a constant velocity of 62 km/h due north. So the displacement is 32 km due north.
- The last 13 km segment is unknown, so let's assume the car moves with a constant velocity of V km/h due north. So the displacement for this segment is 13 km due north.
To calculate the total displacement, we sum up the individual displacements:
Total displacement = 15 km + 32 km + 13 km = 60 km due north
Next, let's calculate the total time taken for the trip. We divide the total distance traveled by the average velocity:
Total time = Total distance / Average velocity
Total distance = 60 km,
Average velocity = 38.5 km/h
Total time = 60 km / 38.5 km/h ≈ 1.558 hours
Now, we can determine the constant velocity for the last 13 km segment by rearranging the formula for average velocity:
Total displacement = Average velocity × Total time
60 km = V km/h × 1.558 hours
Solving for V, we get:
V km/h = 60 km / 1.558 hours = 38.5 km/h.
Therefore, the car travels with a constant velocity of 38.5 km/h due north for the last 13 km segment of the trip.