you live in the middle of a block that is square and one mile around. there is a stop sign on each corner. if your carcan only accelerate and brake at one meter per second per second, describe how you would get around the block in the fastest way.
To determine the fastest way to get around the block, we need to consider the concept of optimal acceleration and deceleration. We'll break down the strategy step by step:
1. Start at one of the corners of the block.
2. Begin driving towards the next corner at a constant speed of 1 meter per second (m/s).
3. As you approach the corner, you need to start planning your deceleration to prepare for the turn. Determine the distance to the next corner, which is the length of one side of the square, i.e., 1 mile or approximately 1609 meters.
4. Let's assume you want to decelerate uniformly in order to stop exactly at the next corner. To calculate the deceleration required, we can use the basic kinematic equation: v^2 = u^2 + 2as, where v is the final velocity (0 m/s since we want to stop), u is the initial velocity (1 m/s), a is the acceleration, and s is the distance to be covered (1609 meters). Rearranging the equation, we get a = (v^2 - u^2) / (2s).
5. Substituting the values into the equation, we find a = (0 - (1^2)) / (2 * 1609). Simplifying, we get a ≈ -6.203 × 10^(-4) m/s^2.
6. Announce the deceleration value to the car's system or set it manually, ensuring the car will smoothly decelerate at a rate of approximately 6.203 × 10^(-4) m/s^2 as you reach the next corner.
7. Complete the turn safely when you arrive at the corner. Remember to yield to other traffic if necessary.
8. Once you've completed the turn, accelerate again to reach the constant speed of 1 m/s.
9. Continue this process for the remaining corners until you reach your starting point.
By following this strategy, you will utilize smooth and efficient acceleration and deceleration to navigate each corner, which should result in the fastest way to get around the block.