Speed of an Object

Speed of an object is defined as the time rate of change of position of the object in any direction, It is measured by the distance travelled by the object in unit time in any direction

speed=(distance travlled)/(time taken)

speed is scalar quantity.It gives no idea about the direction of motion of the object. The speed of the object can be zero or positive but never negetive.

The unit of speed is cms-1 in cgs system and ms-1 in mks system or S.I. The dimensional formula of speed is[M0L1T-1]

Types of Speed

(a) Uniform Speed. An object is said to be moving with a uniform speed, if it covers equal distance in equal interval of time, howesover small these interval may be.

(b) Variable Speed. An object is said to be moving with a variable speed if it covers equal distance in unequal interval of time or unequal distances in equal interval of time, howsoever small these intervals may be

Average Speed When an object is moving with a variable speed, then the average speed oth the object is that constant speed with which the object covers the same distancein a given time as it does while moving with variable speed during the given time. Average speed for the given motion is defined as the ratio of total distance travelled by the object to the total time taken.

Distance and Displacement

Distance.The length of the actual path traversed by an object during motion in a given interval of time is called distance travelled by that object.

Suppose an object goes from Ato C following path ABC, in a certain time t, Then total distance travelled by object in time interval t= AB+BC.

If the object goes from Ato B, B to C and C to A in time t, the total distance travelled by object in time t= AB+BC+CA.

Distance is a scalar quantity. Its value can never be zero or negative, durning the motion of an object

Displacement The displacement of an object in a given interval of time is defined as the shortest distance between the two position of the object in a particluar direction during that time and given by the vector drawn from the initial position to its final postion.

Characteristics of displacement

1.The displacement of anobject has the unit of length.

2.The displacement of an object in a given interval of time can be postive, zero or negative.

3.The magnitude of the displacement of an object between two points gives the shortest distance between those two points.

4.The displacement of an object between two pints has a unique value

5.The actual distance travelled by the object in the given interval can be equal or greater than the magnitude of the displacement.

6.The displacement of an object is unaltered due to the shift in the origin of the postion axis.

Position-time Graph

An object is said to be stationary, if its postion does not change with time. Let the object be stationary at postion x(t)=x from the origin. Then postion-time graph for a stationay object is straight line parallel to the time axis. such a graph describes the train standing at the railway line or bus standing on the road side.

Motion in one, two and three Dimensions

(1) One Dimensional(D) motion. The motion of a object said to be one dimensional motion if only one out of three coordinates specifying the posotion of the object changes with respect to time.

In such a motion, the object moves along a straight line or well defined path. Therefore, one Dimensional motion is sometime known as rectilinear or linear motion.

Example of 1 D. motion of train along a straight railway track, an object dropped from a certain height above the ground, a man walking on a level and narrow raod.

(2) Two Dimensional motion. The motion of a object said to be two dimensional motion if two out of the three coordinates specifying the postion of object changes w.r.t. time. In such a motion, the object moves in plane.

Example of 2 D. an insect crawling over the floor, earth revolving around the sun.

(3) Three Dimensional motion.The motion of a object said to be three dimensional motion of all the three coordinates specifying the position of the object changes w.r.t. time. In such a motion, the object moves in space.

Example of 3 D. a kite flying on a windy day, random motion of gas molecule, a flying aeroplane or bird.

OBJECT IN MOTION

Rest. An object is said to be at rest if it does not change its postion with time, with respect to its sorroundings.

Example of rest body. A book lying on a table, a person sitting in a chair are the example of rest.

Motion. An object is said to be in motion if it changes its position with time, with respect to its sorroundings.

Example of motion body. A bird is flying in air, a man walking on road.

Rest and motion are relative. It means an object in one situation can be at rest but in another situation the same object can be in motion. e.g, a person sitting in a moving train is at rest w.r.t. his fellow passengers but is in motion w.r.t. the objects outside the train. another example is a person sitting in his house is at w.r.t. earth but is in motion w.r.t. other planets.

Types of motion of a body

1)Rectilinear or translatory motion

2)circular or rotatory motion

3)Oscillatory or vibratory motion

1)Rectilinear or translatory motion

Rectilinear motion is that motion in which a particle or point mass body is moving along a straight line.

Translatory motionis that motion in which a body, which is not a point mass body is moving such that all its constiuent particles moves simultaneously along parallel straight lines and shift through equal distance in a given interval of timee.g, A body slipping along the inclined olane has translotary motion.

Rectilinear or translatory motion can be uniform or non-uniform.

2) Circular or Rotatory motion

Circular motion is that motion in which a particle or a point mass body is moving on a circle.

Rotatory motion is that motion in which a body, which is not a point mass body, is moving such that all its constituent particles moves simultaneously along concenric circle, whose centres lie on a line, called axis of rotation and shift through equal angle in a given time.

circular or rotatory motion can be 2D or 3D motion and can be uniform or non-uniform. if the circular or rotatory motion is uniform , it is periodic also.

3)Oscillatory or vibratory motion

Oscillatory motion is that motion in which a body moveto and froor backand forth repeatedlyabout a fixed pointin a definite interval of time. In such a motion the body is confined within well defined limits on either side of means position. It means a periodic and bounced motion of a body about a fixed point is called an oscillatory motion.e.g., the motion of the pendulum of all clock is oscillatory motion.

If in the oscillatory motion, the amplitude is very small i.e,microscopic, the motion of a body is said to be a vibratory motion.

LEARN FREE ABOUT MOTION AND TIME

1.The distance moved by an object in a unit time is called its speed. 2.Speed are of two types non uniform and uniform speed. 3.The measurment of time period is called measurment of time. 4.Pendulum is an example of periodic motion. 5.The time taken by the pendulum to complete one oscillation is called its time period. 6.The basic unit of time is second, minute, hours. 7. The speed of an object is measured by speedometer and the distance covered is measured by odometer.