Question

Can an object be accelerated without speeding up or slowing down? explain?

...........Fast.......

Answer 1

Yes it can.
Acceleration is defined as he rate of change of velocity. If the Velocity is constant then there is no acceleration. Velocity is a vector quantity. Even though there is no change in the speed the velocity may change. The changing direction can even change the velocity. It means that if an object continues to go at the same speed without slowing down or going fast but changes its direction then definitely the velocity changes. As there is a change in velocity the body possess some acceleration.
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Answer 2

This can be answered with an example of circular motion.
When something undergoes circular motion, it's speed remains constant. However, at ever point on the circle the velocity is tangential. Hence the direction keeps changing resulting in a change in the velocity vector. Since there is a change in direction of velocity vector, there is acceleration.
The reason is because velocity and acceleration are vector quantities i.e. They have both magnitude and direction