You\'re speeding at 81km/h when you notice that you\'re only 11m behind the car

Question

You're speeding at 81km/h when you notice that you're only 11m behind the car in front of you, which is moving at the legal speed limit of 60km/h. You slam on your brakes and yor car negatively accelerates at 3.4m/s2.

Q. What will be the distance (x) between the cars be at their closest approach. Assuming the other car continues at constant speed.

Conversions that I did already:

v1: 81km/h = 22.5m/s

v2: 60km/h = 16.6666...m/s

Please provide a solution (step by step) to this problem b/c I really need to learn the in-and-outs of physics.

Explanation / Answer

you need to provide units If I assume everything is in m and seconds the vehicles collide in about a second. Follow this logic through, you will need to change the actual numbers given yourunits; pretend there isn't a collision. call the position of the trailing car x=0 at the moment the brakes are applied, then the equations of motion are x1 = 81t-1/2*4.8t^2 x2=10+60t the difference between them is x2-x1=2.4t^2 -21t +10 this is the equation of a parabola, the extremum in a parabola is given by -b/2a where b is the coefficient of the t term and a is the coefficient of the t^2 term, here this means that the time of minimum approach is t of min approach = 21/4.8 = 4.37s then substitute this into x2-x1 to find the distance of minimum approach

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