A car moves 26km due east then 14km due north. It then turns along a path running north east with 15 km,then 17 km due west.If the time for the journey is 2 hrs,find the average velocity?

Divide the total displacement vector by 2.0 hours

You will have to add four vectors.

I assume you know how to do that by adding components. This is something you should do yourself.

10

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

Step 1: Calculate the displacement in the east direction
The car moves 26 km due east initially, so the displacement in the east direction is 26 km.

Step 2: Calculate the displacement in the north direction
The car moves 14 km due north after the eastward movement, so the displacement in the north direction is 14 km.

Step 3: Calculate the displacement in the northeast direction
The car moves 15 km in the northeast direction. To calculate the displacement in the north and east directions, we can use trigonometry. The displacement in the north direction is given by (15 km) * sin(45°) ≈ 10.61 km, and the displacement in the east direction is given by (15 km) * cos(45°) ≈ 10.61 km.

Step 4: Calculate the displacement in the west direction
The car moves 17 km due west. Since there is no movement in the north or east direction during this segment, the displacement in both the north and east directions is 0 km.

Step 5: Calculate the total displacement
The total displacement in the east direction is 26 km + 10.61 km - 10.61 km = 26 km.
The total displacement in the north direction is 14 km + 10.61 km = 24.61 km.

Step 6: Calculate the average velocity
The total displacement is 26 km in the east direction and 24.61 km in the north direction. The total time taken is 2 hours.
Average velocity = (total displacement) / (total time)
Average velocity = √((26 km)^2 + (24.61 km)^2) / 2 hours
Average velocity ≈ 35.92 km/h

Therefore, the average velocity of the car is approximately 35.92 km/h.