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The definition of 'Uniform motion' in a straight line says that the body covering equal distances in equal intervals of time is to be understood to be in uniform motion. However, can the speed vary within a given interval and still covering the same distance as for any other interval?

e.g. A car travels 10 m in every 4 seconds. In the first 10 m , it covers the first 5 m at a slower speed and the rest 5 m at a faster speed; still being able to cover 10 m in 4 seconds. Is the car executing uniform motion?

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The car is not executing a uniform motion, since it does not cover equal distances in any equal intervals of time. In your example you chose a particular interval of time, 10 sec, in which luckily the car covers always the same distance. But if you chose any other interval (except for 10sec multiples), you would find that the motion is not uniform.

The word any is not specified in the definition you gave, but I think it is tacit.

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You cannot have uniform motion with varying speed. A varying speed creates an accelerated motion. The better way to describe uniform motion in a straight line is the motion at which the instantaneous velocity equals the average velocity at any time interval including that instant.

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Here, first 5m it covers with slower speed Vs and next 5m with faster speed Vf. As per this its average speed mentioned in the question and not uniform speed. So its not uniform motion.

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