Since the velocity of the train is constant at 54kmph, the average velocity is 54kmph.
Proof:
D1 = 54(.5) = 27km.
D1 = 54(.6666666) = 36
Vav = (27 + 36)/1.16666 = 54kmph.
Proof:
D1 = 54(.5) = 27km.
D1 = 54(.6666666) = 36
Vav = (27 + 36)/1.16666 = 54kmph.
D1 = 54• 0.67 = 36 km.
Displacement d =sqrt(D1² + D2)²) = sqrt (27² +36²) =45 km.
Total time is 30+40 =70 min =1.17 hr
Average velocity =displacement/tame taken =>
Average velocity V(ave) = d/t = 45/1.17 =38.57 km/hr.
Note!
Average speed = distance travelled/ time taken =>
Average speed v(ave)= (27+36)/1.17 =53.85 km/hr
Average speed v(ave)= (27+36)/1.17 =54 km/hr
During the first leg of the journey, the train moves eastwards for 30 minutes at a constant velocity of 54 km/h. Since velocity is constant, we can find the displacement using the formula: displacement = velocity x time.
displacement1 = 54 km/h x (30 min / 60 min/h) = 54 km/h x 0.5 h = 27 km.
During the second leg of the journey, the train moves northwards for 40 minutes at the same constant velocity of 54 km/h. Again, using the displacement formula:
displacement2 = 54 km/h x (40 min / 60 min/h) = 54 km/h x 0.67 h = 36 km.
Now, to find the average velocity, we need to consider the total displacement and total time taken. The total displacement is the vector sum of the eastward and northward displacements.
total displacement = √(displacement1^2 + displacement2^2) = √(27^2 + 36^2) = √(729 + 1296) = √2025 = 45 km.
The total time taken is the sum of the time taken for both legs: 30 minutes + 40 minutes = 70 minutes = 1.17 hours.
Finally, we can calculate the average velocity:
average velocity = total displacement / total time taken = 45 km / 1.17 h ≈ 38.5 km/h.
Therefore, the average velocity of the train during the run is approximately 38.5 km/h.