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How would it be possible for an object to be traveling with a constant speed and still accelerating?

Answer :

AL2006
'Acceleration' doesn't mean 'speeding up'.  It means ANY change
in the speed OR direction of motion. 

So, let's say a car is going around a curve, or driving around a
circular track, at a constant speed, its direction is changing, so
its motion is accelerated motion.

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