Physics Word problem

Question

Two cars emerge side by side from a tunnel. Car A is trav- eling with a speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and has an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain your reasoning.

Answer 1

Its seems that these cars are racing.

Speed = initial speed + acceleration multiplied by time

Position = current position + speed multiplied by time + half the acceleration multiplied by time squared. So here is a table that shows what is happening. I show the position at the end of the tunnel as zero and time is in minutes:

Time Car A Position Car A Speed Car B Position Car B Speed

0 0 60 0 40

0.5 35 80 27.5 70

1 80 100 70 100

1.5 135 120 127.5 130

2.0 200 140 200 160

2.5 275 160 287.5 190

So initially, Car A passes Car B but eventually, Car B passes Car A. That assumes the acceleration stays constant.