He travelled 250 m four times: home to shop, shop to home, home to shop and shop to home. Therefore, total distance = 1000 m. Since he returned home, displacement = 0 m.
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The displacement of the athlete will be zero when she returns to the starting point O. In that case, she travels 100 m from O to A and 100 m back to O. Total distance = 200 m.
Yes, the safe distance depends on the speed of the vehicle. As speed increases, the stopping distance increases. Therefore, a vehicle moving faster must maintain a greater distance from the vehicle ahead.
A safe distance should be maintained so that sufficient time and space are available to react and stop safely if the truck suddenly applies its brakes. The required distance depends on speed, reaction time, and braking conditions.
For any chord through A, its length depends on its distance from O. The chord is shortest when this distance is greatest. This occurs when the chord is perpendicular to OA. Hence proved.