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State which of the following situations are possible and give an example for each of these:
$(a)$. an object with a constant acceleration but with zero velocity
$(b)$. an object moving with an acceleration but with uniform speed.
$(c)$. an object moving in a certain direction with an acceleration in the perpendicular direction.
All the given three situations are possible.
$(a)$. An object with a constant acceleration but with zero velocity.
The vertical motion of an object is an example. When an object is thrown upwards and the object reaches its maximum height, the velocity of the body becomes zero, but it still accelerates with constant acceleration$(acceleration\ is\ due\ to\ gravity)$.
$(b)$. An object moving with acceleration but uniform speed.
The Uniform circular motion of an object is an example when the direction of motion of the body is always along the tangent. Here, speed remains constant and the velocity keeps changing as the direction of the body changes. So, acceleration is produced. Hence, we can say that an object moves with acceleration and constant speed in a uniform circular motion.
$(c)$. An object moving in a certain direction with acceleration in the perpendicular direction.
The circular motion of an object is an example of when an object is moving along a circular path. The direction of the body is always perpendicular to its acceleration. But, its acceleration is towards the circle radius. So when the object is in a circular motion, the direction of motion and acceleration are in a mutually perpendicular direction.
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