a train moving at constant velocity of 54 k mph moves east wards for 30 min, then due to north with the same speed for 40 min. What is the average velocity of the train during the run?(in k mph)

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.

D1 = 54• 0.5 = 27km.

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

Last line is

Average speed v(ave)= (27+36)/1.17 =54 km/hr

38.4km/hr

To find the average velocity of the train, we need to calculate the total displacement and divide it by the total time taken.

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.