I am planning to study the Physics chapters as per the study plan that I have given. Only thing I shall do to the extent possible in advance. This study would be of help to me in preparing JEE Level Revision problem set for each chapter.
Today (19.5.2009) I did the following portion
3.1 Rest and Motion
3.2 Distance and displacement
3.3 average speed and instantaneous speed
Worked out examples 1,2
Points to note.
3.1 Rest and Motion
Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.
To identify the rest or motion, we need to locate the position of a particle with respect to a frame of reference. The frame of reference will have three mutually perpendicular axes (X-Y-Z) and the particle can be represented by coordinates x,y,z.
If all coordinates remain unchanged as time passes, we say that particle is at rest. If there is change in any of the coordinates with time, we say the particle or the body represented by the particle is having motion.
I some problems or situations frame of reference is specifically mentioned. Otherwise the frame of reference is understood more easily from the context.
Figure 1: A man with a pistol threatening and asking people not to move.
3.2 Distance and Displacement
If a particle moves from position A to Position B in time t, displacement is the length of the straight line joining A to B. The direction of a vector representing this displacement is from A to B. Displacement is a vector quantity. It has both magnitude and direction.
In the movement between positions A and B the particle may take the path ACB. The length of the path ACB will be distance travelled by the particle. It is only scalar quantity. It has not direction.
3.3 Average speed and Instantaneous speed
The average speed of a particle in a specific time interval is defined as the distance travelled by the particle divided by the time interval.
We can plot the distance s as a function of time. In this graph, the instantaneous speed at time t equals the slope of the tangent at the time t. The average speed in a time interval t to t+Δt become equal to the slope of the chord Δs/Δt. As Δt becomes approaches zero, this average speed becomes instantaneous speed and ds/dt becomes the instantaneous speed.
If we plot a speed versus time graph ( v versus t), the distance travelled in time t (t1 to t2) will be equal to the area bounded by the curve v = f(t), x axis, and the two ordinates t = t1 and t = t2.
In terms of integration it can be represented as s = ∫vdt from t1 to t2