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)

I assume that your "k mph" is really kilometers per hour (km/h)

In 70 minutes, the train goes (1/2)*54 = 27 km east and (2/3)*54 = 36 km north.

It ends up sqrt[(27)^2 + (36)^2]= 45 km from where it started.

The magnitude of the average velocity
is 45 km/(7/6 h) = 38.57 km/h
(70 minutes = 7/6 hour)

The direction of the avg velocity is
arctan 36/27 = 53.13 degrees north of east.

Kmph

To find the average velocity of the train during the run, we need to calculate the total distance traveled and the total time taken.

Let's start by calculating the distance traveled in each direction:

Distance traveled when moving eastwards = velocity x time
Distance = 54 k mph x (30 min / 60 min) = 27 km

Distance traveled when moving northwards = velocity x time
Distance = 54 k mph x (40 min / 60 min) = 36 km

Now, let's calculate the total distance traveled:

Total distance = distance eastwards + distance northwards
Total distance = 27 km + 36 km = 63 km

Next, let's calculate the total time taken:

Total time = time eastwards + time northwards
Total time = 30 min + 40 min = 70 min

Now, let's calculate the average velocity:

Average velocity = total distance / total time
Average velocity = 63 km / (70 min / 60 min) = 54 km/h

Therefore, the average velocity of the train during the run is 54 km/h.