Elementary physics in 1 dimension

[parm12]

The driver of a car wishes to pass a truck that is traveling at a constant speed of 19.0 m/s. Initially, the car is also traveling at a speed 19.0 m/s and its front bumper is a distance 23.7 m behind the truck's rear bumper. The car begins accelerating at a constant acceleration 0.550 m/s^2, then pulls back into the truck's lane when the rear of the car is a distance 25.4 m ahead of the front of the truck. The car is of length 4.90 m and the truck is of length 21.8 m. How much time is required for the car to pass the truck?

I'm having trouble understanding why 13.5 s is incorrect.

Here is my approach:

T_position = 19(m/s)t + 50.4m (50.4 = Car length + Truck Length + Distance in beteen)
C_position = .275(m/s^2)t^2 + 19(m/s)t

C_position corresponds to the rear of the car, and T_position the front of the truck.

Solving for both position equations yields:

50.4m = .275(m/s^2)t^2

sqrt(50.4/.275) = t = 13.5s

[Galileo]

They're probably asking when the car pulls back into the same lane as the truck. Then the car will have completed his manouver to pass the car, not when the car's rear is at the truck's front.
It isn't specifically mentioned, but from the information given in the question, it's highly certain.

[parm12]

You were correct, but I do feel misled by the question. The time it takes a particle to pass another particle is at the time t when the distances are equivalent (assuming the same conditions for motion as in this problem). It is afterwards from this time that one particle will be "passed" the other.

Thanks much for the input :approve: