A car travels West for 20min at 80km/hr and in direction 45NW at 30km/hr for 6min. Calculate the Total distance covered/ displacement of the car/ average speed/ average velocity.

west =(1/3)hour*80 + (1/10)hr* 30 * cos 45

north = (1/10)*30 * sin 45

distance = sqrt(north^2+west^2)

displacement = distance at angle T north of west where tan T = north/west

speed = distance/ (1/3+1/10)

velocity = speed at angle T

To calculate the total distance covered by the car, we need to add up the distances traveled in each direction.

1. Distance traveled in the west direction:
Time = 20 min = 20/60 = 1/3 hr
Speed = 80 km/hr
Distance = Speed × Time = 80 km/hr × 1/3 hr = 80/3 km

2. Distance traveled in the 45NW direction:
Time = 6 min = 6/60 = 1/10 hr
Speed = 30 km/hr
Since the car is traveling in a diagonal direction, we need to find the horizontal and vertical components of the speed.
Horizontal component = Speed × cos(45°)
Vertical component = Speed × sin(45°)

Horizontal component = 30 km/hr × cos(45°) = 30 km/hr × √2/2 = 15√2 km/hr
Vertical component = 30 km/hr × sin(45°) = 30 km/hr × √2/2 = 15√2 km/hr

Distance in the NW direction is found using the horizontal component:
Distance = Horizontal component × Time = 15√2 km/hr × 1/10 hr = 3√2/2 km

Now, let's calculate the requested results:

Total distance covered = Distance in the west direction + Distance in the NW direction
Total distance covered = 80/3 km + 3√2/2 km

To find the displacement of the car, we need to calculate the net horizontal and vertical distances. The net horizontal distance is obtained by subtracting the horizontal components of distance.
Net horizontal distance = Distance in the west direction - Horizontal component of distance in the NW direction
Net horizontal distance = 80/3 km - 15√2 km/hr × 1/10 hr

To find the net vertical distance, we need to add the vertical components of distance because both directions are positive.
Net vertical distance = Vertical component of distance in the NW direction
Net vertical distance = 15√2 km/hr × 1/10 hr

To calculate the average speed, we need to divide the total distance covered by the total time taken.
Total time = Time in the west direction + Time in the NW direction
Total time = 20 min + 6 min = 26 min = 26/60 = 13/30 hr

Average speed = Total distance covered / Total time
Average speed = (80/3 km + 3√2/2 km) / (13/30 hr)

To calculate the average velocity, we need to divide the total displacement by the total time taken.
Average velocity = Net horizontal distance + Net vertical distance / Total time

Now you can plug in the values and calculate each result!