# 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 $v_1$ ??

• Your vehicle needs its brakes fixed!
– Matt
Apr 27, 2011 at 10:05

## 1 Answer

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 $v1$?

• to the question i answer to v1 would be zero. but the problem is. the scenario might differ. i mean initial velocity, initial speed, target velocity, target required speed, time to target etc.. they may change. Apr 27, 2011 at 10:45