Constant acceleration car problem

[acg7160]

Homework Statement

You're speeding at 85 km/h when you notice that you're only 10m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car decelerates at 4.2 m/s^2. Assuming the car in front of you continues at constant speed, will you collide? if so, at what relative speed? if not what will the distance between the cars at their closest approach?

Homework Equations

I know I have to use x=x0+v0t+(1/2)at^2 but I am not sure exactly what numbers go where.

The Attempt at a Solution

For car 1 I think x0=0 ; v0=85 km/h (converting to m/s=23.6) and a=-4.2 (decelerating) and for car 2 x0=10 ; v0=60 km/h or 16.67 m/s and a=0? so do i plug those into two separate equations of my x equation in the relevant equations part and then solve for t? and then does t show if they collide or not?

I am not good at physics and need help please!

 

[acg7160]

Please help!

 

[berkeman]

Homework Statement

You're speeding at 85 km/h when you notice that you're only 10m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car decelerates at 4.2 m/s^2. Assuming the car in front of you continues at constant speed, will you collide? if so, at what relative speed? if not what will the distance between the cars at their closest approach?

Homework Equations

I know I have to use x=x0+v0t+(1/2)at^2 but I am not sure exactly what numbers go where.

The Attempt at a Solution

For car 1 I think x0=0 ; v0=85 km/h (converting to m/s=23.6) and a=-4.2 (decelerating) and for car 2 x0=10 ; v0=60 km/h or 16.67 m/s and a=0? so do i plug those into two separate equations of my x equation in the relevant equations part and then solve for t? and then does t show if they collide or not?

I am not good at physics and need help please!

I think I'd start by calculating how long it takes in time for the faster car to slow to the speed of the slower car, and then figure out what their positions are at that time. That will tell you if they hit or not. Then I would go on with the rest of the problem.