Should I Attempt the Pass? Kinematics Problem on a Car

[Bashyboy]

Homework Statement

A car is behind a truck going 25 m/s on the highway. The car's driver looks for an oportunity to pass, guessing that his car can accelerate at 1.0 m/s^2. He gauges that he has to cover the 20 m length of the truck, plus 10 m clear room at the rear of the truck and 10 m at the front of it. In an oncoming lane, he sees a car approaching, probably also traveling at 25 m/s. He estimates that the car is about 400 m away. Should he attempt the pass?

I know the displacement of the truck is x = 25 m/s*t

and that the displacement of the car is x = 25 m/s*t + 1/2(1.0 m/s^2)t^2.

I have this feeling that I am suppose to set this two equations equal to each other, and then solve for time, which will give me the time the car passes the truck. But I can't seem to figure out why this is true. What does it mean, physically, setting these two equations together?

Also, I try to preview my post, but it won't display latex, so I don't even know if I typed it in correctly. How do I get around this?

 

[Bashyboy]

Am I perhaps looking too deeply into this? I just feel that I need logical justification so that I may not just remember that it's suppose to be this way, but I can use reason.

 

[LawrenceC]

"I have this feeling that I am suppose to set this two equations equal to each other, and then solve for time, which will give me the time the car passes the truck."

If you set the two equations equal to one another and solve for time, you get zero for the time. The car has to travel a greater distance than the truck in the same amount of time.

The problem states nothing about how much the passer should clear the oncoming car. How badly does the passer want to scare the approaching car's driver? When you scare other drivers, their reactions are unpredictable.

 

[zabachi]

I can see the latex when i preview the post. Do you type in the latex urself or use the Latex refernce?

 

[Bashyboy]

I type it in myself, because there were some symbols I couldn't find.