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Yes, it is possible for a body to accelerate, without changing the speed. Bodies in circular motion are continuously accelerating.Even if they don't change their speed, their velocity is constantly changing due to continuous change in direction of motion.
And we know a body accelerates when there is change in velocity. 
Therefore bodies in circular motion are having constant speed yet undergo acceleration.
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Yes it is possible for a body to be accelerated withour speeding up or slowing down.a body moving on curved path or a circular path with uniform speed produces change in velocity and hence gets accelerated.
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