Motion in 1D problem, it's not supposed to be this hard.

[Executioner]

Homework Statement

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 91.0 km/hr approaches a car stopped at the red light. When the truck is 115.7 meters from the car the light turns green and the car immediately begins to accelerate at 2.90 m/s^2 to a final speed of 106.0 km/hr. How close does the truck come to the car assuming the truck does not slow down?

Homework Equations

I might be wrong but I've used this formula:
Vo = "V knot"
Xo = "X knot" (initial position)

X = (1/2)at^2 + Vot + Xo

The Attempt at a Solution

I convert the trucks velocity from 91 km/hr into 25.278 m/s, and I've converted the car's final velocity to 29.44 m/s. I tried to do the above equation for both vehicles and set them equal to each other so I'll know what time they meet. I was thinking this way and then when I find TIME, I'll plug it in back into one of the "X = (1/2) etc" equation to find the distance.

My professor doesn't show us any examples, all he did was just show us how we get the equation. Thanks guys for any help, I really appreciate it.

 

[ehild]

The problem asks the minimal distance the truck approaches the car. If you find a time when they meet it means that the truck and the car will collide. Just think: The truck goes with uniform speed. The car accelerates from zero speed. Its speed increases, reaches that of the truck and gets even higher up to 106 km/h. Up to what speed will the distance decrease between them?

ehild

 

[novop]

The truck is gaining on the car right up until the cars speed > the trucks speed. At what time does the cars speed equal the trucks speed? Where are the truck and car at this time?

 

[Executioner]

Thanks guys, so at some point the car AND the truck both have the same velocity right?

 

[ehild]

Thanks guys, so at some point the car AND the truck both have the same velocity right?

Yes, and you have to find that moment.

ehild

 

[Executioner]

OK, so the car will hit the speed of 25.278 (which is the same like the truck) at some time T right? I find that T and then plug it back into the position equation for each of the vehicles right? After that subtract the two and I get how much farther (closest) they are apart?

 

[Executioner]

Awesome! I got it! I knew it had something to do with time when they both has the same velocity! You just confirmed it and helped me out! Thank you so much guys! :)

 

[ehild]

Congratulation! Good job!

ehild