summary of chapter motion class 9.
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CBSE Class 9 Science Revision Notes Chapter 8 Motion
Motion occurs when an object changes its position with time.
When a body covers equal distance in equal interval of time, it is moving with uniform motion.
When a body covers unequal distance in equal interval of time. it is moving with non-uniform motion.
Both Distance and Time are important in describing motion.
Sometimes you know motion has occurred even if you didn’t see it happen.
Relative motion: when two objects are moving in a plane (either in same direction or opposite) each have relative motion with respect to second. e.g. a person sitting in a train and watching a tree, in this case tree is stable but is assumed to be moving but with respect to train.
Distance vs. Displacement
Distance: How far an object has moved. It has only magnitude without direction.
Displacement: How far and in what direction an object has moved from its start position. i.e. the direct distance between intial and final points.
Speed
Speed = the distance an object travels in a given amount of time
SI unit of speed is m/s
Types of Speed
Constant speed: speed doesn’t change
Changing speed: Riding a bike for 5 km. Take off and increase speed, slow down up hill, speed up down hill, stop for stop sign. The trip took you 15 min (.25 h)
Average speed =
Instantaneous speed: speed at any given time.
Velocity
Velocity: includes speed and direction.
Storm is moving at 20km/hr.
Suppose two trains are going with the same speed in opposite direction so they are having different velocities.
Race car going around an oval track might have constant speed, but different velocities at each point.
Acceleration
Any change in velocity over a period of time is called acceleration.
The sign (+ or -) of indicates its direction. + sign shows the acceleration and – sign shows de-acceleration.
Uniform (constant) acceleration equation
a = v/t
Images of car are equally spaced.
The car is moving with constant positive velocity (shown by red arrows maintaining the same size) .
The acceleration equals to zero
Images of car become farther apart as time increases
Velocity and acceleration are in the same direction
Acceleration is uniform (Arrows below the car maintain the same length)
Velocity is increasing (Arrows above the car are getting longer)
This shows positive acceleration and positive velocity
The instant speed at points of equal elevations is the same.
The velocities are different because they are in opposite free fall & air resistance.
Galileo Galilei Italian physicist and astronomer Formulated laws of motion for objects in free fall
A freely falling object is any object moving freely under the influence of gravity alone.
It does not depend upon the initial motion of the object
Dropped – released from rest
Thrown downward
Thrown upward
The acceleration of an object in free fall is directed downward, regardless of the initial motion
The magnitude of free fall acceleration (gravitational acceleration) is g = 9.80
g decreases with increasing altitude
g varies with latitude, height and depth from earth surface.
9.80 is the average at the Earth’s surface
The italicized g will be used for the acceleration due to gravity
Not to be confused with g for grams
With negligible air resistance, falling objects can be considered freely falling. objects of different shapes accelerate differently (stone vs feather)
Speed both upward and downward
The path is symmetrical.
Acceleration is constant.
The magnitude of the velocities is the same at equal heights.
Images become closer together as time increases
Acceleration and velocity are in opposite directions when ball goes upward.
Acceleration is uniform (violet arrows maintain the same length)
Velocity is decreasing in upward motion (red arrows are getting shorter)
Positive velocity and negative acceleration
Velocity becomes zero at maximum height.
Time duration flight in going upward and coming back is always same.
2 Graphical Representation Of Motion & Graphs
3. Equation of motion
(1) When object is moving in straight line-
Average acceleration describes how fast the velocity is changing with respecttime.
where:
= average acceleration
v = change in velocity
x = displacement
t = elapsed time
(2) when object is coming vertically downward-
(3) when object is coming vertically upward-
The SI unit of velocity is the m/s.
Average acceleration is+ or – depending on direction.
Instantaneous Acceleration
Instantaneous acceleration is the limit of approaches zero
Instantaneous acceleration is zero where slope is constant
Instantaneous acceleration is positive where curve is concave up
Instantaneous acceleration is negative where curve is concave down
Uniform Circular Motion
In this kind of motion the object moves on circle with fix speed but the direction changed by the time so the velocity of the change so its called acceleration motion acceleration is called centrifugal acceleration.It is directed toward the centre.
Explanation:
Notes for Motion
Graph's :
Distance�Time Graphs
• For a body at rest
• As the slope is zero, so speed of the body is zero.
• For a body moving with uniform speed
• For accelerated motion.
• The slope of graph is increasing with time
• For decelerated (speeding down) motion.
• Slope of graph is decreasing with time
Velocity�Time Graphs
• When a body moving with a uniform velocity.
• The slope of AB indicates zero acceleration
• When a body starts from rest and moves with uniform acceleration.
• Greater is the slope of v-t graph, greater will be the acceleration
• When a body is moving with uniform acceleration and its initial velocity is not zero.
• When a body is moving with increasing acceleration.
• Slope increases with time.
• When a body is moving with decreasing acceleration.
• Slope decreases with time.
• When a body is moving with a uniform retardation and its initial velocity is not zero.
• As θ > 90°, graph has a negative slope.
Facts that Matter
• An object is said to be in motion when its position changes with time.
• We describe the location of an object by specifying a reference point. Motion is relative. The total path covered by an object is said to be the distance travelled by it.
• The shortest path/distance measured from the initial to the final position of an object is known as the displacement.
• Uniform motion: When an object covers equal distances in equal intervals of time, it is said to be in uniform motion.
• Non-uniform motion: Motions where objects cover unequal distances in equal intervals of time.
• Speed: The distance travelled by an object in unit time is referred to as speed. Its unit is m/s.
• Average speed: For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object by the total time taken.
• Velocity: Velocity is the speed of an object moving in definite direction. S.I. unit is m/s.
• Acceleration: Change in the velocity of an object per unit time.
• Graphical representation of motions
(i) Distance-time graph
For a distance-time graph time is taken on x-axis and distance is taken on y-axis.
[Note: All independent quantities are taken along the x-axis and dependent quantities are taken along y-axis.]
OA = CD = u
OE = CB = v
OC = AD = t
BD = BC – DC (Change in velocity)
AD is parallel to OC.
∴ BC = BD + DC = BD + OA
∴ BC = v and OA = u
We get v = BD + u
∴ BD = v – u ...(1)
In velocity-time graph, slope gives acceleration.
Substituting (2) in (1) we get
BD = v – u
at = v – u
∴ v = u + at
(ii) Equation for position-time relation:
Let us assume,
s = distance travelled by the object
t = in time t
a = with uniform acceleration.
∴ Distance travelled by the object is given by area enclosed with OABC in the graph.
∴ s = OABC
= (area of rectangle OADC) + (area of DABD)
Substituting
OA = u, OC = AD = t and BD = at
We get
(iii) Equation for position-velocity relation:
s = distance travelled by the object
t = in time t
a = moving with uniform acceleration
s = area enclosed by trapezium OABC
Substitute value of ‘t’ in (1)
• Uniform circular motion: When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.