Kinematics Physics equation, simple explanation.

[LeopardGecko]

You are stuck behind a slow driver, there is a 1 km passing lane between a slow car and a truck. In order to properly pass you must be at least 40m from the slow car. You are traveling at 70km/h and there is an oncoming truck traveling at 80km/h. Each car is 4m long. What is the minimum acceleration you would need.

Figuring out the final answer isn't the problem, just the manipulation of the next equation to find maximum time it would take. I don't get how this works out, could somebody should me step by step on how to turn d = vt into:

d = v(car)t + d + v(truck)t

Basically what two equations does he combine together to make this equation up above?

Entering numerical values makes it:

1000m = v(you)t + 44 + v(truck)t

 

[Redbelly98]

d = v(car)t + d + v(truck)t

Are you sure you wrote the same equation as you saw it? This equation simplifies to

v(car) = v(truck)​

which is wrong.

 

[LeopardGecko]

Yeah, it is exactly as I saw it. Minus where I added in car and truck in parenthesis, but that was implied by the question.

The next step in the equation is

956 = t(70+80)

Which makes doesn't make sense as this is now the total distance you have to pass when you're beside the other car and doesn't account for the time that you and the truck had moved by the time "your" car had moved up to the "slow car".

It would make sense if when the variables where entered it would be 1044m = t(70+80).