Two cars travel along a level highway. It is observed that the distance between the cars is increasing . Which one of the following statements concerning this situation is necessarily true ?

Options

A. The velocity of each car is inceasing.
B. At least one of the cars has non-zero acceleration.
C. The trailing car has the smaller acceleration.
D. Both cars could be accelerating at the same rate.

Answer

To solve the problem, we need to analyze the situation where two cars are traveling along a level highway and the distance between them is increasing. We have to determine which statement is necessarily true among the given options.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have two cars moving along a straight path (level highway).
- The distance between the two cars is increasing, which means that the car behind is either moving faster than the car in front or the car in front is moving slower than the car behind.

2. **Analyzing the Statements**:
- We have four statements to evaluate:
1. The velocity of each car is increasing.
2. At least one of the cars has non-zero acceleration.
3. The trailing car has the smaller acceleration.
4. Both cars could be accelerating at the same rate.

3. **Evaluating Each Statement**:
- **Statement 1**: "The velocity of each car is increasing."
- This is not necessarily true. The car behind could have a constant speed while the car in front is moving at a slower constant speed, which would still result in an increasing distance. Therefore, this statement is incorrect.

- **Statement 2**: "At least one of the cars has non-zero acceleration."
- This is also not necessarily true. Both cars could be moving at constant velocities (zero acceleration), and if the car behind is faster, the distance would still increase. Thus, this statement is incorrect.

- **Statement 3**: "The trailing car has the smaller acceleration."
- This is not necessarily true either. The trailing car could have a higher acceleration but still be behind if it started from a lower speed. Hence, this statement is incorrect.

- **Statement 4**: "Both cars could be accelerating at the same rate."
- This statement can be true. If both cars are accelerating at the same rate but the car in front has a higher initial speed, the distance between them can still increase. Therefore, this statement is potentially true.

4. **Conclusion**:
- The only statement that holds true under the given conditions is **Statement 4**: "Both cars could be accelerating at the same rate." This is the correct answer.

### Final Answer:
The correct statement is: **4. Both cars could be accelerating at the same rate.**