Question

Suppose two cars are travelling north along a road. Car 1 travels at a constant speed of50 mph for two hours, then speeds up and drives at a constant speed of 100 mph forthe next hour. The car breaks down and the driver has to stop and work on it for twohours. When he gets it running again, he continues driving recklessly at a constantspeed of 100 mph.Car 2 starts at the same time that Car 1 starts, but Car 2 starts 100 miles farther norththan Car 1 and travels at a constant speed of 25 mph throughout the trip.

Sketch the distance-versus-time graphs for Car 1 and Car 2 on a coordinate plane and determine how many times the two cars will pass by each other during their trips.

Answer 1

Car 1 and Car 2 will pass each other multiple times during their trips, depending on the specific time when Car 1 breaks down and gets back on the road.

Step-by-step explanation:

In order to determine how many times Car 1 and Car 2 pass each other during their trips, we need to analyze their distance-versus-time graphs.

For Car 1, we know that it travels at a constant speed of 50 mph for 2 hours, then speeds up to 100 mph for 1 hour. It then breaks down for 2 hours before continuing at a constant speed of 100 mph.

For Car 2, it starts 100 miles farther north than Car 1 and travels at a constant speed of 25 mph throughout the trip.

To sketch the distance-versus-time graphs for both cars, we need to consider the distance covered during each segment of their trips and the time spent in each segment.

Overall, Car 2 will pass Car 1 during its initial acceleration and during the segment when Car 1 is broken down while Car 2 is still traveling. The number of times they pass each other will depend on the specific time when Car 1 breaks down and gets back on the road.