Motion and Time
3.1 Introduction
In our daily life, we see various objects in motion. The walking man, the running cars, the water flowing in lakes, flying aeroplanes etc. are all examples of objects in motion.
- A body is said to be in motion if it changes its position with respect to a reference point.
- Motion and rest are relative terms for e.g. If A and B are sitting in a moving car and a third person C is standing outside than A and B are at rest w.r.t. each other but in motion w.r.t. C. - Speed is defined as distance travelled per unit time i.e. speed = distance/time
–Uniform motion – A body is said to have uniform motion if it moves with constant speed in same direction.
- Non uniform motion – A body is said to have non uniform motion if either speed or direction of the moving body changes.
- Average speed = total distance travelled /total time taken (for non-uniform motion)
-S.I unit of speed is m/s.
- Speed = distance/time
- Distance = speed x time
- Time = distance / speed
MEASUREMENT OF TIME-
- All of the clocks make use of some periodic motion. One of the most well-known periodic motions is that of a simple pendulum.
- The to and fro motion of a simple pendulumis an example of oscillatory motion which is a periodic motion.
- The time taken by a pendulum to complete one oscillation is called its time period.
- The basic unit of time is second.
3.2 Rest and Motion
Rest: A body is said to be in rest if it does not change its position with respect to time with respect to another body. Example-A book lying on a table.
Motion: A body is said to be in motion if it changes its position with respect to time with respect to another body. Example-A train moving on rails, a man walking on road.
3.3 Physical quantities
Physical quantity : The quantity which can be measured is called physical quantity. In Physics, we study about physical quantity.
Types of physical quantity
i) Fundamental physical quantity
ii) Derived physical quantity
Fundamental physical quantity : The physical quantities which are independent of other physical quantities are called fundamental physical quantities. Example : Lenth, Mass, Time etc.
Derived physical quantity: The physical quantities which depend on fundamental physical quantities are called derived physical quantities. Example : Speed, Energy etc.
All physical quantities can be categorised into scalars and vectors.
Scalars: The quantities which have magnitude only are called scalars. Example : Distance, Speed, Energy etc.
Vectors: The quantities which have magnitude as well as directions both are called vectors.
Examples : Displacement, Velocity, Force etc. A vector is represented by putting an arrow over symbol of the phycal quantity like velocity is represented as v r , force is represented as F , etc r
3.4 Speed
We know that some vehicles move faster than others. The distance moved by objects in a given interval of time can help us to decide which one is faster or slower.
Speed can be defined as the distance covered by an object in a unit time. Thus
Speed = Total distance covered / Total time taken
The S.I. unit of speed is m/s and it is a scalar quantity.
3.5 Velocity
The velocity of an object is the ratio of total displacement to the total time taken. Thus Velocity = Total displacement /Total time taken
The S.I. unit of velocity is similar to that of speed as m/s but velocity is a vector quantity, because it also determines the direction of motion.
3.5 Acceleration
The acceleration of a moving object is defined as the rate of change in its velocity with time. Thus
The S.I. unit of acceleration is m/s2 and it is a vector quantity.
3.6 Types of motion :
(a) Uniform Motion : If an object is moving along a straighty line with constant speed/velocity, it is said to be in uniform motion.
for Uniform motion : Velocity = constan
So, for uniform motion acceleration is 0.
Equation of motion for uniform motion :
Distance/Displacement = speed × time = velocity × time
Note: For uniform motion along a straight line, speed and velocity are same. Similary, distance and displacement are also same for the above mentioned case.
(b) Non-uniform motion : If the velocity of an object keeps on changing with time, the motion is said to be non-uniform. Since, the velocity of the object is not constant, therefore, it possesses acceleration. So, depending on the acceleration, motion can be further of two types:
(i) Uniformly accelerated motion : Where the acceleration of the body remains constant.
(ii) Non-uniformly accelerated miotion : Where the acceleration of the body keeps on changing with time.
Equations of motion for uniformly accelerated body :
3.8 Distance time graph
The distance-time graph is a line graph. Let us learn to make such a graph. Take a sheet of graph paper. Draw two lines perpendicular to each other on it, as shown in figure given below:
Mark the horizontal line as XOX’. It is known as the x-axis. Similarly mark the vertical line YOY’. It is called the y-axis. The point of intersection of XOX’ and YOY’ is known as the origin O. You can make the graph by following steps given below:
Draw two perpendicular lines to represent the two axes and mark them as OX and OY as in given figure. Decide the quantity to be shown along the x-axis and that to be shown along the y-axis. In this case we show the time along the x-axis and the distance along the y-axis. Choose a scale to represent the distance and another to represent the time on the graph. For the motion of the car scales could be
Time : 1 min = 1 cm. Distance: 1 km = 1 cm. Mark values for the time and the distance on the respective axes according to the scale you have chosen. Now you have to mark the points on the graph paper to represent each set of values for distance and time. The corresponding figure shows the set of points on the graph corresponding to positions of the car at various times.
Joint all the points on the graph. This is the distnace time graph for the motion of the car. If the distance-time graph is a straight line, it indicates that the object is moving with a constant speed. However, if the speed of the object keeps changing, the graph can be of any shape.
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