IIT JEE Blogs

• The position of object can change on a straight line (like on x-axis with respect to origin) or on a plane with respect to some fixed point or frame. So we can define motion as follows:
• An object or a body is said to be in motion if its position continuously changes with time with reference to a fixed point (or fixed frame of reference)
• When the position of object changes on a straight line i.e. motion of object along straight line is called motion in one dimension.
• To understand the essential concepts of one dimensional motion we have to go through some basic definitions.
• One can see the platform from a running train, and it seems that all the objects placed on platform are continuously changing their position. But one, who is on platform, concludes that the objects on the platform are at rest. It means if we will take the train as reference frame the objects are not stationary and taking reference frame as platform the objects are stationary. So the study of motion is a combined property of the object under study and the observer. Hence there is a need to define a frame of reference under which we have to study the motion of an object. We can define the frame of reference as follows:
• A frame of reference is a set of coordinate axes which is fixed with respect to a space point (a body or an object can also be treated as a point mass and therefore it can become a site for fixing a reference frame), which we have arbitrarily chosen as per our observer’s requirement. The essential requirement for a frame of reference is that, it should be rigid.
• The position of an object is defined with respect to some frame of reference. As a convention, we define position of a point (essentially we treat body as a point mass) with the help of three co-ordinates X, Y and Z. Hence (X, Y, Z) is a set of coordinate axes representing a 3-dimensional space and each point in this space can be uniquely defined with the help of a set of X, Y and Z coordinate, all three axes being mutually perpendicular to each other. The line drawn from origin to the point represents the position vector of that point.

In the figure 2.1, the position of a point P is specified and

is called the position vector.

• Consider a case in which the position of an object changes with time. Suppose at certain instant ‘t’ the position of an object is x₁ along the x axis and some other instant ‘T’ the position is x ₂ then the displacement Δx is defined as

Δx = x₂ – x₁

• It can be seen in the figure 2.2 where x₁ and x₂ are instantaneous position of the object at time t and T respectively.
• Now consider the motion of a point A with respect to a reference point O. The motion of point A makes its radius vector vary in the general case both in magnitude and in direction as shown in figure 2.3. Suppose the point A travels from point 1 to point 2 in the time interval Δt.

Distance and Displacement

• To understand the difference between distance and displacement, we study the motion of vertical throw of a ball with respect to point O to height h.
• After some time it will come again to the same point O. The displacement of ball is zero but there is some distance traversed by the ball. It’s because distance is a scalar quantity but displacement is a vector quantity.

Speed and Velocity

• Speed is the rate of change of distance without regard to directions. Velocity is the rate at which the position vector of a particle changes with time. Velocity is a vector quantity whereas speed is scalar quantity but both are measured in the same unit m/sec.