To analyze the situation where two cars are traveling along a level straight highway and the distance between them is increasing, we need to consider the concepts of velocity and acceleration. Let's break down the options provided to determine which statement is true.
Understanding the Scenario
In this scenario, we have two cars: a leading car and a trailing car. The fact that the distance between them is increasing indicates that the trailing car is either moving slower than the leading car or that the leading car is accelerating faster than the trailing car.
Evaluating the Statements
- A. Velocity of each car is increasing: This statement could be true for both cars, but it doesn't necessarily explain why the distance between them is increasing. Both cars could be accelerating, but if they are accelerating at the same rate, the distance would not change.
- B. Leading car has greater acceleration: This could be a valid statement. If the leading car is accelerating faster than the trailing car, it would increase the distance between them. However, we cannot definitively say this is true without more information.
- C. Both cars may have the same acceleration: If both cars have the same acceleration, the distance between them would remain constant, not increase. Therefore, this statement is not true in this context.
- D. The trailing car has smaller acceleration: This statement is likely true. If the trailing car has a smaller acceleration than the leading car, it would not be able to catch up, resulting in an increasing distance between the two cars.
Conclusion on the Correct Statement
Based on the analysis, the most accurate statement regarding the situation is D. The trailing car has smaller acceleration. This is because for the distance between the two cars to be increasing, the trailing car must not be able to keep up with the leading car's speed or acceleration. If the trailing car had the same or greater acceleration, the distance would either remain constant or decrease.
Real-World Analogy
Think of it like two runners on a track. If one runner (the leading car) is sprinting ahead while the other runner (the trailing car) is jogging, the gap between them will widen. Even if both runners are moving forward, the one who is sprinting (leading car) is accelerating faster than the one who is jogging (trailing car), which perfectly illustrates the situation described.
In summary, the key takeaway is that for the distance between the two cars to increase, the trailing car must have a smaller acceleration compared to the leading car. This understanding of acceleration and velocity is crucial in analyzing motion in physics.
