Car's maximum velocity in a straight then deceleration!

We are doing a project to find the quickest time round a given track in a car.
friction: k=1.6
mass of car m=750kg
power of engine w=350kw
distance x=500m

After a corner, the car comes out at velocity=31.9m/s
There is a 500m straight next but have to finish it at 31.9m/s for next corner.
I need to know the fastest way to complete the 500m.
how can i work out the maximum velocity i can go and when to start braking?
i think we found the braking eqaution was a=-gk but we are basically really stuck!
any help would be greatly appreciated!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution


Science Advisor
Homework Helper
Welcome to PF!

Hi leathley! Welcome to PF! :smile:

Call the maximum speed v …

then use the appropriate constant acceleration equation twice, once to find the distance needed to accelerate up to that speed, and once to find the distance needed to decelerate under braking back to 31.9m/s …

then choose v so that the distances add up to 500m :wink:
distance needed to get to vmax, s = (vmax^2 -vi^2)/2a or what???

can't just do the reverse for the other distance because s1 + s2 will cancel each other out.

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