A car starts from x = 0 at a constant speed of 13 m/s for 22 s. Then it decelerates at 2 m/s2 until it stops. Returning along the same track with an acceleration of 1.8 m/s2 for 10 s, what average speed has the car had until that moment?

To find the average speed of the car until the moment it returns along the same track, we need to break down the motion into three segments: 1. Constant speed for 22 seconds. 2. Deceleration until the car stops. 3. Acceleration for 10 seconds. First, let's calculate the distance traveled during each segment: 1. Constant speed: Distance = Speed × Time Distance = 13 m/s × 22 s = 286 m 2. Deceleration until stopping: To find the time it takes to stop under deceleration, we can use the formula: Final velocity squared = Initial velocity squared + 2 × acceleration × distance 0 (final velocity) = (13 m/s)^2 + 2 × (-2 m/s^2) × distance Solving for distance: 169 m = 4 × distance distance = 169 m / 4 = 42.25 m So, the car stops after traveling 42.25 meters during deceleration. 3. Acceleration for 10 seconds: To find the distance during acceleration, we can use the formula: Distance = Initial velocity × Time + 0.5 × acceleration × Time^2 Distance = 0 m/s (starting from rest) × 10 s + 0.5 × 1.8 m/s^2 × (10 s)^2 Distance = 0 + 0.5 × 1.8 m/s^2 × 100 s^2 = 90 m Now, let's calculate the total distance traveled during these three segments: Total distance = Distance at constant speed + Distance during deceleration + Distance during acceleration Total distance = 286 m + 42.25 m + 90 m = 418.25 m Now, we'll find the total time taken for this journey: Total time = Time at constant speed + Time during deceleration + Time during acceleration Total time = 22 s + (time to stop) + 10 s To find the time it takes to stop during deceleration, we can use the formula: Final velocity = Initial velocity + (acceleration × time) 0 m/s = 13 m/s - 2 m/s^2 × (time to stop) 2 m/s^2 × (time to stop) = 13 m/s time to stop = 13 m/s / 2 m/s^2 = 6.5 s Now, we can calculate the total time: Total time = 22 s + 6.5 s + 10 s = 38.5 s Now, we can find the average speed: Average speed = Total distance / Total time Average speed = 418.25 m / 38.5 s ≈ 10.86 m/s So, the average speed of the car until the moment it returns along the same track is approximately 10.86 meters per second.