A train moving with constant speed of 54kmph moves eastwards for 30min then north for 40min find avg velocity
Average velocity = displacement/ total time
Train travels 1/2 h * 54 km/ h E = 27 km E
Train travels 2/3 h * 54 km/ h N = 36 km N
A rough sketch of the above displacement vectors is helpful: use the Pythagorean Theorem to find the magnitude of the resultant displacement, and basic trig to find its direction.
Divide the resultant displacement by the total time (1/2 h + 2/3 h) to get average velocity.
Remember displacement and velocity are vectors. Include the direction. tan(angle east of north) = distance east/distance north
To find the average velocity, we need to divide the total displacement by the total time taken.
First, let's calculate the displacement in the eastward direction. The train's speed is given as 54 km/h, and it moves for 30 minutes, which is 0.5 hours. Therefore, the displacement in the eastward direction is:
Displacement in the eastward direction = Speed × Time = 54 km/h × 0.5 hours = 27 km
Next, let's calculate the displacement in the northward direction. The train moves north for 40 minutes, which is 0.67 hours. However, the speed of the train doesn't affect the displacement in the northward direction since it's moving at a constant speed. Therefore, the displacement in the northward direction is:
Displacement in the northward direction = 0 km (since speed doesn't affect the displacement in North/South direction)
Now, we can calculate the total displacement by finding the vector sum of the eastward and northward displacements. Since the displacement in the northward direction is zero, the total displacement is equal to the eastward displacement:
Total displacement = Displacement in the eastward direction = 27 km
Next, let's calculate the total time taken by summing the time taken to move in the eastward and northward directions. The train moves eastward for 30 minutes and then northward for 40 minutes, so the total time taken is:
Total time = Time taken to move eastward + Time taken to move northward = 30 minutes + 40 minutes = 70 minutes = 1.17 hours
Finally, we can calculate the average velocity by dividing the total displacement by the total time taken:
Average velocity = Total displacement / Total time = 27 km / 1.17 hours ≈ 23.08 km/h
Therefore, the average velocity of the train is approximately 23.08 km/h.