Question

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 acceleration but uniform speed.
(c) An object moving in a certain direction with acceleration in the perpendicular direction.

Answer 1

Hint: Acceleration of a body is the change in velocity divided by change in time. Velocity and acceleration are vector quantities. Since a vector quantity has both magnitude and direction, while explaining these quantities, we need to consider their directions as well. Circular motion and vertical motion of a body can be used to explain the situations given in the question.

Complete step-by-step solution
All three situations are possible.
(a) An object with a constant acceleration but with zero velocity.
Change in velocity is known as acceleration. One example of this is the vertical motion of an object. When the object is thrown upwards and reaches the maximum height, the velocity of the body becomes zero, but it still accelerates with constant acceleration. The constant acceleration is due to gravity.

(b) An object moving with acceleration but uniform speed.
Considering the uniform circular motion of a body, the direction of motion of the body is always along the tangent. Here, speed is constant. Since the velocity is a vector quantity, it keeps changing as the direction of the body changes. Since, the change in velocity is acceleration, as the velocity changes 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.
Consider the circular motion of an object. When the object is moving along a circular motion its path is along the tangent. The direction of the body is always perpendicular to its acceleration. But, its acceleration is towards the circle radius. So when the object in a circular motion, the direction of motion and acceleration are in a mutually perpendicular direction.

Note: Speed is the magnitude of a velocity. Even if speed is not changing, the velocity of an object can be changed by changing its direction. If the speed of a body is changed, velocity is changed; hence the acceleration also changes.