Optimizing Rally Race Time with Maximum Acceleration and Deceleration

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In summary, the problem is to find the minimum time required for a pilot to travel a straight road of 1 km in a rally race, starting and ending at zero speed, with a maximum acceleration of 2.5 m/s^2 and a maximum deceleration of -3.8 m/s^2. The attempt at a solution involved setting up equations of motion and using the fact that the total distance traveled is equal to 1 km, but the method did not yield a solution. After further attempts, the problem was successfully solved.
  • #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?
 
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  • #2
No matter, I solved it :D sorry for posting
 

1. How does optimizing rally race time with maximum acceleration and deceleration improve performance?

By maximizing acceleration and deceleration, the car can reach its top speed faster and brake more efficiently, allowing for quicker turns and overall faster lap times. It also allows for better control and maneuverability on different terrains.

2. What factors should be considered when optimizing rally race time?

Some important factors to consider include the car's horsepower, weight and distribution, tire grip and pressure, suspension, and driver skill. The terrain and weather conditions also play a significant role in determining optimal acceleration and deceleration strategies.

3. How do you determine the best acceleration and deceleration settings for a specific rally race?

It is crucial to test and adjust the acceleration and deceleration settings during practice runs to find the optimal balance for the specific race track and conditions. Data analysis and feedback from the driver can also help determine the best settings for maximum performance.

4. Can optimizing rally race time with maximum acceleration and deceleration be harmful to the car?

While pushing the car to its limits can put additional strain on the engine and other components, proper maintenance and tuning can minimize potential damage. It is essential to have a skilled mechanic regularly check and maintain the car to ensure its longevity and safety.

5. Are there any safety concerns when optimizing rally race time with maximum acceleration and deceleration?

Safety should always be a top priority in any motorsport, and rally racing is no exception. It is crucial to have proper safety measures in place, such as a roll cage, racing harness, and fire extinguisher, to protect the driver in case of an accident. It is also essential to have a well-maintained car and to follow all safety protocols and regulations set by the race organizers.

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