In this post we are going to show the detailed solution for class 9th science chapter 8. All the solution are prepared by our esteemed who are very well experienced in the teaching.
Summary of the Chapter :
Motion : Movement of any object from one position to another position with respect to the observer is called a Motion.
Position : Motion of any object is defined by its position with respect to the observer. Position is the located of the object. If object changes its position with the passage of time, it is said to be in motion.
Reference point : It is the point from which the location of object is measured. It is often called as origin.
Any object can be located only with the help of reference point and its direction.
Example : Suppose a person changes its position with respect to a tree (a reference point) with passage of time. In this example, person is an object and tree is a reference point. Direction is also necessary to locate an object.
Motion in straight line : When an object moves in straight line with respect to the observer then the motion is called straight line motion. For example, motion of lift.
Vector and scalar quantity
Vector quantity : Vector is a quantity which have both magnitude and direction.
Examples : Force, position, velocity, displacement, etc.
Scalar quantity : Scalar is a quantity with which direction is not associated.
Examples : Speed, distance etc.
Note: Magnitude of vector only represents numerical value of the vector without its direction.
Distance and Displacement
Distance is the actual path travelled by an object from its initial position to final position. It is a scalar quantity.
Displacement is the shortest straight line path between initial and final position.
- If the initial and final points are same then displacement will be zero.
- Distance depends on path but displacement does not.
- Distance is always greater than or equal to displacement. They are equal only in straight line motion without taking U – turn.
Uniform and Non Uniform motion
Uniform motion is a motion in which equal distance is covered in equal time intervals.
Non Uniform motion is a motion in which unequal distance is covered in equal intervals of time.
Speed and Velocity
Speed is the distance travelled by object in unit time.
Speed Formula = Distance travelled / Time taken
Average Speed : The ratio of total distance travelled to the total time taken by the body gives its average speed.
Average Speed Formula = Total Distance Travelled / Total Time Taken
It is a scalar quantity. The SI unit of speed is meter/sec.
Velocity is the displacement of body in unit time.
Velocity is a vector quantity. The SI unit of velocity is meter/sec.
Velocity Formula = Displacement of object / Time Taken
Note:
- Velocity has both magnitude and direction while speed has only magnitude and no direction.
- Velocity has same direction as displacement.
Average Velocity : The ratio of total displacement travelled to total time taken by the body gives its average velocity.
Average Velocity Formula = Total Displacement / Total Time Taken
Note :
- Average speed is always greater than average velocity expert in case of straight line motion without U – turn when both are equal.
- If body return to its initial position, average velocity will be zero but average speed will not be zero.
- When direction of motion changes, velocity also changes.
Acceleration
Acceleration is measure of change of velocity with time. It is also called rate of change of velocity. The SI unit of acceleration is meter/sec². It is a vector quantity.
Acceleration = Final velocity – Initial velocity / Total Time Taken
If the velocity of an object changes from an initial value u to the final value v in time t, the motion is called acceleration motion. In this case, acceleration a is given by
= a = (v – u)/ t
Acceleration motion is a motion in which acceleration is not equal to zero.
- Acceleration has same direction as of velocity if velocity increases.
- Acceleration has opposite direction as of velocity if velocity decreases . In this case, acceleration will be negative. Negative acceleration is also called Retardation/ De – acceleration.
Uniform and Non – Uniform acceleration
- When velocity of body changes by equal amounts in equal time intervals, acceleration is said to be uniform.
- When velocity of body changes by unequal amounts in equal intervals on time, acceleration is said to be non – uniform.
Falling of ball is a uniform motion. Motion of car is a non – uniform motion.
Equations of Uniform Accelerated Motion
Relation among velocity, distance, time, and acceleration is called equations of motion. There are three equations of motion for bodies moving with uniform acceleration.
First Equation of motion :
= v = u + at…. (i)
Second Equation of motion :
= s = ut + ½ at²…. (ii)
Third Equation of motion :
= v² – u² = 2as….(iii)
Here,
v = Final velocity of the body
u = Initial velocity of the body
t = time period of the body
a = acceleration of the body
s = distance travelled by the body in time t.
Average Velocity in Uniform Accelerated Motion
If a body moves ‘s ‘ distance in ‘t’ time interval . Then,
Average Velocity = Displacement / Time
= s/t
= (ut + ½at²) /t [ ∴ s = ut + ½ at² ]
= ut + ½ at
= ut + ½ (v-u)
= u + v/2 – u/2
= u/2 + v/2 = u + v/2
Here ‘a’ is uniform acceleration of body.
Graphical Representation of Motion
To describe the motion of an object, we can see different graphs. Graphical representation of motion shows dependence of one physical quantity such as distance, velocity on other quantity such as time.
Graphical Representation of Motion
1. Distance Time Graphs:
The change in the position of an object with time can be represented on the distance – time graph. The distance time graph for a moving body can be used to calculate speed of the body.
1. Straight line graph : The distance time graph for a body moving at uniform speed is always a straight line as body in uniform motion, body moves equal distance in equal time intervals.
2. Curved graph : When graph of distance Vs time is plotted for an object moving with non uniform speed, the slope of graph will not be a straight line. The rising trend of slope shows the increasing trend of velocity.
3. The distance – time graph is parallel to time axis when the body is at rest.
2. Velocity – time graph:
- If a body moves with a uniform velocity (no acceleration) then speed time graph for this body would be straight line parallel to time axis.
- If body moves with a non uniform velocity (uniform acceleration) then speed time graph would be a straight line. The pattern of slope of the graph depends on sign of velocity.
Circular Motion :
Uniform circular motion is the motion in which an object moves on a circular path with constant speed. For example: watch, moon revolve around earth etc.
Non – uniform circular motion is the motion in which an object moves on a circular path with varying speed.
When an object is in circular motion, direction of its velocity keeps on changing.
Speed in the case of circular motion
Suppose a body is moving in a circular path of radius r.
Speed (v) = distance /time
= Circumference of circle / time
= 2 πr / t
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