Spherical Geometry Distance Between 2 Points

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I try to calculate distance between 2 points on Earth. I have an a car and this car goes with speed 100 km/h and I know the start point latirude and longitude and car goes 5 hours. I want to calculate "How far has the vehicle traveled?". Actually answer is so simple I know distance = speed * time . However does this rule apply to spherical geometry? I am not sure.

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If the vehicle is traveling along the surface of the sphere, then yes: $distance = speed * time$.