Motion In A Straight Line

Introduction

This is the most common word we are using in our daily life, like we run, walk and ride a motor cycle. Vehicles like bus, planes, train carry peoples from one place to other. Birds are fling in sky, animals wandering in a jungle. In the above examples we can find that every object change its position with respect to time or object is moving from one place to other with time.

In this session we will study how to describe motion. There are different types of motion we have linear(rectilinear)motion, circular motion, vibration motion. In all these types of motion we have to take objects as point objects. That is size of the object should be small compare to the distance it moves in a given time.

Position, Distance and Displacement

Position

A bus is moving from A to B. Here A and B indicates the starting position and end position of a bus. To specify the position of an object, we needs reference point and a set of axes. So consider a rectangular coordinate system consisting of three perpendicular axes X, Y and Z axes.  The intersection point of all these three axes at origin (O) called reference point. The coordinates system along with time constitutes a frame of reference.

Distance (Path length)

Let us take example that a train is moving along a straight line. Here we need only one axis to define how the train is changing the position from one place to other with time.

Above figure shows the motion of a train at different position at different instant of time.

O is the starting point of a train that is x=0 at t=0. Let A and B be the position of the train at different instant of time. Train moves from O to A.so distance traveled by the train is  OA=10m. That is actual path traveled by the train is called distance or path length. As the train moves further to B then total distance traveled is OA+AB=20m. Distance is a scalar quantity.

Displacement

Shortest distance between two position of an object at a given time along particular direction or difference between the final and initial position of an object.

Let x1 and x2 be the position of an object at time t1 and t2.

If an object moving along the straight line covers equal distances in equal intervals of time is called uniform motion.

We can represent uniform motion of an object graphically by plotting a graph in which position along y-axis and time along x axis.

Average speed and Average velocity

Total distance traveled by an object divided by total time taken is called average speed.

The SI unit of both average speed and average velocity is m/s or ms-1.

If an object moving along a straight line and in the same direction then magnitude of displacement is equal to the total path length. In such a case the magnitude of average velocity is equal to the average speed.

If an object moving along a straight line and during this motion suppose an object change its direction so that path length is greater than magnitude of displacement. In such a case speed is greater than the magnitude if velocity.

Instantaneous velocity and instantaneous speed

In last topic average velocity  and average speed we understood how fast an object moving over a given time interval, but it doesn’t tells about how fast an object moving at different instant of time. For this we define a terms Instantaneous velocity and instantaneous speed.

Instantaneous velocity can be defined as the limiting value of average velocity as the time interval becomes infinitesimally small.

Above equation says the rate of change of position with respect to given instant of time.

Instantaneous speed at any instant is equal to the magnitude of instantaneous velocity at that instant.

Acceleration

We know that all motor vehicles have a device called accelerator, which is mainly used to change the velocity. When an object moving along a straight line, the velocity in general changes with time. So rate of change of velocity is called acceleration.

The average acceleration is defined as the change of velocity divided by the time interval.

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