Optimal Speed Limit?

📌 CONCEPT: The problem requires finding the optimal speed limit on the road such that the total travel time from City A to City B is minimized, given that the car accelerates uniformly from rest to reach a top speed of 80 km/h in 5 minutes.

📐 RULE / FORMULA: We can use the concept of average speed and the formula for uniformly accelerated motion to find the optimal speed limit.

💡 WORKED EXAMPLE: Let's assume the optimal speed limit is 'v' km/h. The time taken to travel from City A to City B with this speed limit will be the sum of the time taken to accelerate from 0 to 80 km/h and the time taken to travel the distance at the optimal speed. Using the formula for uniformly accelerated motion, we can find the optimal speed limit 'v' that minimizes the total travel time.

⚠️ COMMON MISTAKE: Students often forget to consider the time taken for acceleration and deceleration, which can lead to incorrect solutions.