# Deccelerate and Accelerate to achieve timed journey

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 $v_1$ ??

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Your vehicle needs its brakes fixed! – Matt Apr 27 '11 at 10:05

If you graph the velocity as a function of time, then the area under the graph gives the distance traveled. If the speed doesn't change at all, then you hit the target in 20 seconds. You need to hit it in 40 seconds, so your graph will be twice as wide, so it should be (on average) half as high. What does that tell you about $v1$?