A horse rider covers half the distance with 5 m s⁻¹ speed. The remaining part of the distance is travelled with speed 10 m s⁻¹ for half the time and with speed 15 m s⁻¹ for the other half of the time. The mean speed of the rider averaged over the whole time is x/7 m s⁻¹. The value of x is:
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 1 Morning Shift

Question

A horse rider covers half the distance with 5 m s⁻¹ speed. The remaining part of the distance is travelled with speed 10 m s⁻¹ for half the time and with speed 15 m s⁻¹ for the other half of the time. The mean speed of the rider averaged over the whole time is x/7 m s⁻¹. The value of x is:

Physics · Circular Motion

JEE Mains 30 January 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Let each half of total distance be x₀. Time for first half = x₀/5. In the second half, equal times at 10 and 15 m s⁻¹ give average speed 12.5 m s⁻¹, so time = x₀/12.5 = 2x₀/25. Total distance = 2x₀ and total time = x₀/5 + 2x₀/25 = 7x₀/25. Thus mean speed = 2x₀/(7x₀/25) = 50/7 m s⁻¹, so x = 50.