Final answer:
At the moment the car passes by the observer, the distance is increasing at a rate of 25 m/s. Twenty seconds later, the rate at which the distance is increasing is less than 25 m/s because the car is no longer moving perpendicular to the line from the observer to the car.
Step-by-step explanation:
When a car travels down a highway at 25 m/s and passes by an observer standing 150 m from the highway:
- (a) The rate at which the distance from the observer to the car is increasing is 25 m/s at the moment the car passes in front of the observer. This is because the car is moving perpendicular to the line from the observer to the car, thus the entire velocity of the car contributes to the rate at which the distance is increasing.
- (b) Twenty seconds later, the car has moved farther down the highway and is no longer moving perpendicular to the line from the observer to the car. At this point, only the component of the car's velocity that increases the distance between the car and the observer contributes to the rate at which the distance is increasing; hence, the rate of increase in the distance is less than 25 m/s. However, the exact rate would require a calculation involving right triangle trigonometry, as the situation forms a right triangle where the distance from the observer to the highway is one leg, the distance the car has traveled since passing the observer is the other leg, and the hypotenuse is the distance from the observer to the car.