Question

Can a body have constant speed but still accelerating explain.

Answer 1

Yes, A body can have constant speed but still accelerate as in case of uniform circular motion. 

In uniform circular motion speed remains constant and direction of velocity changes with every point in the direction of tangent drawn from that point.
Therefore Speed remains same but velocity varies making the body accelerate.

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Answer 2

Yes, Of course a body can have constant speed but still accelerating.

See,
Acceleration is the rate of change of velocity so when velocity changes, it is an accelerated motion.

Let's take eg. uniform circular motion. In this motion the particle changes it's direction at every point so velocity changes. As velocity changes it is an accelerated motion.
But the speed remains same at every point because it is uniform circular motion .....so speed is constant.

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