- #1
Bestfrog
Homework Statement
In a rally race a pilot must travel in a minimum time ##t## a road long ##d=1 km## (the road is straight). Before he starts he is still and he must end still (so the speed at start and end is zero). The maximum acceleration is ##a_1=2,5 ms^{-2}## and the maximum deceleration is ##a_2=-3,8 ms^{-2}##. Find the minimum time t.
The Attempt at a Solution
I tried to solve it by constructing a system of the equations of motion $$d_1=\frac{1}{2} a_1 t_1^2$$
$$d_2= v_1 t_2 -\frac{1}{2}a_2 t_2^2= a_1t_1t_2 -\frac{1}{2}a_2 t_2^2$$
And I used the fact that ##d_1+d_2=d## but I can't conclude. I tried to solve it with AM-GM inequality but it doesn't work, so I think that these are the wrong paths to solve this simple problem. Any hint?
