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

Last updated date: 14th Jun 2024
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Hint: Analyse the questions properly and answer them by providing everyday examples. Try to recall what you mean by constant acceleration, uniform speed and how to determine the direction of acceleration and other terms.

Complete step by step answer:
Let’s start with what do we mean by the terms like constant acceleration, zero velocity, uniform speed etc. Constant acceleration means that the rate of change of velocity in a course of time is constant or in other words we can say that the velocity-time graph is a straight line.

A body is said to be moving with uniform speed, if it covers equal distances in equal intervals of time. The displacement-time graph is a straight line. When we say that acceleration vector is perpendicular to velocity vector, we mean that the angle between these vectors is a right angle. Now that we know the meanings of each term let’s look at the examples.

Let’s throw a ball directly upwards from the surface of earth. Now this ball will have an initial velocity which will constantly decrease and become zero at the highest point of its trajectory. At this point, its velocity is zero but it has a constant acceleration due to gravity \[g = 9.8m{s^{ - 2}}\]. So this explains how an object can have constant acceleration but zero velocity.

When we tie a stone to a string and move it in circular motion, the direction of motion is always along the tangent. Therefore the speed of the motion is always constant. But due to change in direction of the tangent the velocity of the stone continuously changes. And we know that the rate of change of velocity is known as acceleration. Thus when velocity changes acceleration is produced in uniform circular motion but with uniform speed.

As we know, the direction of velocity and acceleration constantly changes in uniform circular motion. The direction of velocity is along the tangent of the path of uniform circular motion and the direction of acceleration is along the radius of the circular path from the moving object towards the centre. And in a circle a tangent is always perpendicular to its radius joining the point of contact of the tangent and the centre. Thus in uniform circular motion, the direction of acceleration is perpendicular to the direction of velocity.

Note: These types of questions require conceptual understanding and how do you approach the problem. Just keep in mind the very definitions and how basic things work in classical mechanics. A very good exercise for a student will be to try and find out other examples that we encounter in our daily lives.