A girl is riding her scooter and finds that its speedometer reading is constant. Is it possible for her scooter to be accelerating and if so, how?

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Yes. The speedometer shows only the magnitude of velocity (speed). If the scooter turns , the direction of its velocity changes even though the speed is constant. A change in velocity (here, in direction) means the scooter is accelerating — just like in uniform circular motion.

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