This question appears to be very simple at first but has stumped me for hours now: we are given 2 accelerations +7.5m/s^2 and -10m/s^ a car brakes and accelerates at these rates over 105m, what is the maximum velocity the car will reach, starting and stopping at rest? Originally I was thinking to use one of the three constant acceleration equations but I always end up going nowhere (0=0, 7.5t=10t) etc. The closest I've gotten was plotting a velocity-time graph but I can think of no way to find the constant to be added onto the line -10t to make the area under it and 7.5t equal 105m. I believe I just have to use the formula v^2 = vi^2 + 2(s-si) but every time I try I'm stuck! If some1 can point me in the right direction itd be of awesomeness! Thank you for your time.