Calculating Passing Time of Accelerating Car and Bus

[1irishman]

Homework Statement

A car of length 4m and a bus of length 12m are traveling in the same direction 20m apart. The cars current velocity is 10m/s and the buses current velocity is 20m/s, the car suddenly starts to accelerate at 5m/s^2 and stops accelerating after 5 seconds. How long does it take the car to completely pass the bus?

Homework Equations

d=Vit + 1/2at^2
i'm not sure about other ones that can be used here...

The Attempt at a Solution

I figured (not sure if it's right though) the bus travels 100m in 5s and the car travels 112.5m in the same amount of time. So the original distance of 20m between the car and the bus has lessened to 20m - 12.5m = 7.5m. So the distance between the bus and the car is now 7.5m. Not sure how to proceed from here...hints? Thanks.

 

[Delphi51]

I see no mention of the 2 seconds in the question.
The 112.5 m is correct for the car at time 5 s. Good start.

 

[1irishman]

i figured (not sure if it's right though) the bus travels 100m in 5s and the car travels 112.5m in the same amount of time. So the original distance of 20m between the car and the bus has lessened to 20m - 12.5m = 7.5m. So the distance between the bus and the car is now 7.5m. Not sure how to proceed from here...hints? Thanks.

 

[Delphi51]

Well, the car stopped accelerating after 5 s, so both vehicles must now be in motion at constant speed. The next bit should be easier . . .
Don't forget the lengths of the vehicles!

 

[1irishman]

after 5s the new constant speed of the car should be 35m/s right? And the total distance should now be 23.5m right?

 

[1irishman]

okay...i think I've solved it:
since cars new constant speed is 35m/s and distance is 23.5m.
The relative speed to the bus should be 15m/s.
So, v=15m/s
d=23.5m
then t=1.6s
So, it should take the car 6.6s to pass the bus right?

 

[Delphi51]

Very nicely done! Congrats.

 

[1irishman]

Thanks!