Sandy races her sister to get home. If they use different routes will the winner have the greatest average speed or greatest average velocity?

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Sandy is on a race with his sister to reach home. The two of them take different paths.

The person who wins the race is the one who can reach home from the starting point in the shortest amount of time. Velocity reflects the value of the displacement from where they start to their home divide by the time taken. Speed is the total distance travelled divided by the total time taken. If one of them were to take a longer path, it would mean spending a longer duration of time to reach the same destination. This would mean a higher average speed but the same average velocity.

This gives us the result that the person who reaches home first and wins the race is the one with the greatest average velocity rather than the one with the greatest average speed.

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