I have a vehicle traveling at initial speed 100m/s. Expected destination speed is also $100m/s$. Maximum deceleration is $3$. Maximum acceleration is $10$. Distance to the target is $2000m$. The vehicle should reach the target in $40s$.
The vehicle should follow a linear path, decelerate($a_1$) to a certain speed(v1) and accelerate back($a_2$) to reach the target precisely on $40s$.
Note: $v_1 > 0, a_1 < 3, a_2 < 10$.
How do we find $a_1$, $a_2$ and $v_1$ ??