Average speed =total distance /timelet the distance travelled from A to B= x kmthen,total distance travelled = 2x kmtime while going from A to B = D/s=x/30 hourstime while returning = x/50 hourstotal time = x/30 + x/50  =(5x+ 3x)/150          =8x/150                  =4x/75 hoursaverage speed = (2x x 75)/4x                            =37.5 km/hr

Answer:

Given:
Speed from A to B = 30 km/h
Speed from B to A = 50 km/h



(a) Displacement of the car:
- Displacement is the shortest distance between the initial and final point of an object.
- As the car starts from point A and returns back to point A, the displacement of the car will be zero.
- Hence, the displacement of the car is 0 km.

(b) Distance travelled by the car:
- Distance is the total length of the path travelled by an object.
- Distance from A to B = 80 km (as distance = speed × time and time is not given, we cannot calculate the time taken to travel from A to B)
- Distance from B to A = 80 km (same distance as A to B)
- Total distance travelled by the car = distance from A to B + distance from B to A = 80 + 80 = 160 km

(c) Average speed of the car:
- The average speed of an object is the total distance travelled by the object divided by the total time taken.
- As the time taken to travel from A to B and from B to A is not given, we cannot calculate the average speed of the car.
- However, we can find the average speed of the car for the entire journey (from A to B and back to A) using the formula:

Average speed = (total distance travelled)/(total time taken)

- Total distance travelled = 160 km (from part (b))
- Total time taken = (time taken from A to B) + (time taken from B to A)

- Let d = distance from A to B
- Let t1 = time taken from A to B
- Let t2 = time taken from B to A

d = 30t1 (equation 1)
d = 50t2 (equation 2)

- From equation 1 and 2, we get:

t1 = d/30
t2 = d/50

- Total time taken = t1 + t2 = (d/30) + (d/50) = (5d + 3d)/150 = 8d/150

- Substituting the values in the formula for average speed, we get:

Average speed = (160)/(8d/150) = 150/3 = 50 km/h

- Hence, the average speed of the car for the entire journey is 50 km/h.