A car is moving along a straight (OP). It moves from `O to P` in `18 seconds` amd retuns from `P to Q` in 6 seconds`, where `OP=360 m` and `OQ=240 m What are the car the average velcoty and average speed of the car in going (a) from `Oto P` and back to `Q` ?

Options

A. velocity
B. acceleration
C. work done
D. The averge velocity of the car in going for a particle in a given interval of time represents

Explanation

To solve the problem, we need to calculate the average velocity and average speed of the car as it moves from point O to point P and then back to point Q.

### Step 1: Understand the distances and times
- Distance from O to P (OP) = 360 m
- Distance from P to Q (PQ) = OQ - OP = 240 m - 360 m = -120 m (since Q is behind P)
- Time taken from O to P = 18 seconds
- Time taken from P to Q = 6 seconds

### Step 2: Calculate total distance traveled
Total distance traveled by the car:
- Distance from O to P = 360 m
- Distance from P to Q = 120 m (the absolute value since we consider distance)
- Total distance = 360 m + 120 m = 480 m

### Step 3: Calculate total time taken
Total time taken for the journey:
- Time from O to P = 18 seconds
- Time from P to Q = 6 seconds
- Total time = 18 s + 6 s = 24 s

### Step 4: Calculate average speed
Average speed is defined as the total distance traveled divided by the total time taken.
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{480 \, \text{m}}{24 \, \text{s}} = 20 \, \text{m/s} \]

### Step 5: Calculate total displacement
Displacement is the shortest distance from the initial position to the final position.
- Initial position (O) = 0 m
- Final position (Q) = 240 m
- Total displacement = OQ - OP = 240 m - 0 m = 240 m

### Step 6: Calculate average velocity
Average velocity is defined as the total displacement divided by the total time taken.
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{240 \, \text{m}}{24 \, \text{s}} = 10 \, \text{m/s} \]

### Final Answers:
- Average Speed = 20 m/s
- Average Velocity = 10 m/s