Motion and Time

The following points should be kept in mind while choosing most suitable scale for drawing a graph

• The difference between the highest and the lowest values of each quantity.
• The intermediate values of each quantity to mark the values on the graph.
• To utilize the maximum part of the paper on which graph is to be drawn.

Distance-time graphs gives information about the nature of the motion of an object like uniform or uniform motion. Motion of an object can be represented by its distance-time graphs.

The distance covered by a moving object is the actual length of the path followed by the object is called. Distance is a scalar quantity. SI unit of distance is meter. But Displacement is the shortest distance covered by a moving object from the point of reference (initial position of the body), in a specified direction.

An object is said to be moving with uniform speed if it covers equal distances in equal intervals of time. But when we travel in a vehicle the speed of the vehicle changes from time to time depending upon the conditions existing on the road. In such a situation, the speed is calculated by taking the ratio of the total distance travelled by the vehicle to the total time taken for the journey. This is called the average speed.

An object is said to be moving with variable speed or non-uniform speed if it covers equal distances in unequal intervals of time or vice-versa.

When we say that the car travels at an average speed of 60 km/h it does not mean that the car would be moving with the speed of 60 km/h throughout the journey. The actual speed of the car may be less than or greater than the average speed at a particular instant of time. The speed of a moving body at any particular instant of time is called instantaneous speed.

On a see-saw child goes up and comes down from mean position and repeats itself .So there is oscillatory motion.

In ancient time the time between one sunrise and the next was called a day. A month was measured from one new moon to the next and a year was fixed as the time taken by the earth to complete one revolution of the sun.

Velocity can be defined as the rate of change of displacement.SI unit of velocity is m/s (meter/second Velocity is a vector quantity.

It is a special type of clock or watch which have an electric circuit with one or more cells are called quartz clocks.

By finding the distance travel by a moving body in unit time 1 hr. or 1 sec we know the speed of an object that help us to know which one is moving faster i.e. having greater speed.

The time taken by pendulum to complete 1 oscillation is called time period
The time taken by pendulum to complete 5 oscillation = 15sec
The time taken by pendulum to complete 1 oscillation = 15/5= 3 sec
So time period = 3 sec

We know distance travelled by a body = speed X time
So, distance travelled by the car =5x4=20 km

Total distance travelled =2.4km=2.4x1000m=2400m. Speed is 6m/sec
as time = (Distance/speed) time=2400/6= 400sec.

We have observed that the position of stars and planets change while you remain stationary. In reality the earth is moving too. Thus, an object which appears to be at rest, may actually be in motion. Therefore, motion and rest are relative terms.

Motion of an object in a circular path is called circular motion eg. Motion of the hands of a clock. But when an object repeats its motion after some time. This type of motion is called periodic motion. E.g. Motion of a pendulum, motion of a child on a swing, motion of the strings of a guitar.

The motion of a ball on the ground. Here the ball is rolling on the ground and rotating as well as moving forward on the ground. Thus, the ball undergoes a rectilinear motion as well as rotational motion.

A simple pendulum consists of a small metallic ball or a piece of stone suspended from a rigid stand by a thread .The metallic ball is called the bob of the pendulum.

One complete to and fro motion of a pendulum from rest position is called one oscillation. The time taken by the pendulum to complete one oscillation is called its time period. It is only depending on the length of the string of pendulum.

Following are different types of motion:

• Translatory Motion: - In Translatory motion the particle moves from one point in space to another. This motion may be along a straight line or along a curved path.
• Rectilinear motion : Motion along a straight line is called rectilinear motion. Example: A car moving on a straight road
• Curvilinear motion: Motion along a curved path is called curvilinear motion. Example: A car negotiating a curve
• Rotatory Motion : In rotatory motion, the particles of the body describe concentric circles about the axis of motion
• Vibratory Motion: In vibratory motion the particles move to and fro about a fixed point.

The interval between two events is called time. Example: The time between one sunrise and the next was called a day. Clocks or watches are the most common time measuring devices. The basic unit of time is a second. Its symbol is s. Larger units of time are minutes (min) and hours (h).

To plot a graph on a graph sheet:
Take a graph paper. At the centre of the paper, draw two lines perpendicular to each other Mark the point of intersection of the lines as ‘O. The horizontal line is called the X-axis, while the vertical line is called the Y-axis. The point of intersection of the two axes is called the origin, "O". Take one quantity along the X-axis and the other along the Y-axis, after choosing suitable scales for both. For every value along one axis, mark a point matching the related value on the other axis. Join the points, and your graph is ready.

Time taken to complete 20 oscillations = 32 s
Time period of the pendulum = No of oscillations/Total Time taken = 32/20 s = 1.6s

Initial reading of car odometer= 57321.0 km
Final reading of car odometer= 57336.0 km
Time at the time of Initial reading= 08:30 AM
Time at the time of Initial reading= 08:50 AM
Distance travelled by the car = 57336.0 km - 57321.0 km
= 15 Km
Time taken by the car to cover distance = 08:50 AM -08:30 AM
= 20 m
Speed of the car in Km/m = 15 km/20m
= .75 Km/m
Speed of the car in Km/h = 15 km/20m X 60
= 45 Km/h

Distance between her school and house = speed of bicycle X Time taken
= 2m/s × 60s= 1800m

The distance between two stations = 300 km
Time taken by the train to cover that distance = 6 hours
Speed of the train = 300/6 Km/h =50 km/h

The vehicle A is moving faster as distance represented by vertical axis of A is more as compare to B for a given point of time.

Distance covered by the car with a speed
of 40 km/h in 15 minutes = Speed X Time
= (40 Km/h /60 minute) X 15 minute
Distance covered by the car with a speed
of 40 km/h in 15 minutes = Speed X Time
= (60 Km/h /60 minute) X 15 minute
= 15 Km
Total distance covered by the car =(10 + 15 )km = 25 Km