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(Home», Revision Notes»Class 9 Science»Motion, For Example, a new…
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For Example, a new restaurant is opening shortly at a distance of 5 km north from my house. Here, the house is the reference point that is used for describing where the restaurant is located.
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Distance – The distance covered by an object is described as the total path length covered by an object between two endpoints.
Distance is a numerical quantity. We do not mention the direction in which an object is travelling while mentioning about the distance covered by that object.
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According to the figure 1 given above, if an object moves from point O to point A then total distance travelled by the object is given as 60 km.
Displacement – The shortest possible distance between the initial and final position of an object is called Displacement.
Consider the figure 1 given above, here the shortest distance between O and A is 60 km only. Hence, displacement is 60 km.
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Zero Displacement – When the first and last positions of an object are same, the displacement is zero.
For Example, consider the diagrams given below.
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Here, displacement of object B is negative
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Also, displacement of object A is positive
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Hence, distance is a scalar quantity while displacement is a vector quantity.
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Displacement can be positive, negative or zero
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When an object travels equal distances in equal intervals of time the object is said to have a uniform motion.
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When an object travels unequal distances in equal intervals of time the object is said to have a non-uniform motion.
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Formula of Distance, Time and Speed
Average Speed – If the motion of the object is non-uniform then we calculate the average speed to signify the rate of motion of that object.
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For Example, If an object travels 10m in 3 seconds and 12m in 7 seconds. Then its average speed would be:
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To describe the rate of motion in a direction the term velocity is used. It is defined as the speed of an object in a particular direction.
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The magnitude of speed or velocity at a particular instance of time is called Instantaneous Speed or Velocity.
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Uniform Motion – In case of uniform motion the velocity of an object remains constant with change in time. Hence, the rate of change of velocity is said to be zero.
Non-uniform Motion – In case of non-uniform motion the velocity of an object changes with time. This rate of change of velocity per unit time is called Acceleration.
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Acceleration is also a vector quantity. The direction of acceleration is the same if the velocity is increasing in the same direction. Such acceleration is called Positive Acceleration.
The direction of acceleration becomes opposite as that of velocity if velocity is decreasing in a direction. Such acceleration is called Negative Acceleration.
De-acceleration or Retardation – Negative acceleration is also called De-acceleration or Retardation
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The graph in case the object is stationary (means the distance is constant at all time intervals) – Straight line graph parallel to x = axis
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Constant velocity – Straight line graph, velocity is always parallel to the x-axis
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Consider the graph given below. The area under the graph gives the distance traveled between a certain interval of time. Hence, if we want to find out the distance traveled between time interval t1 and t2, we need to calculate the area enclosed by the rectangle ABCD where area (ABCD) = AB * AC.
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Similarly, to calculate distance traveled in a time interval in case of uniform acceleration, we need to find out the area under the graph, as shown in the figure below.
To calculate the distance between time intervals t1 and t2 we need to find out area represented by ABED.
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The equations of motion represent the relationship between an object's acceleration, velocity and distance covered if and only if,
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- The Equation for Velocity – Time Relation
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- The Equation for Position – Time Relation
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- The Equation for the Position – Velocity Relation
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Initial velocity, u can be derived from velocity at point P or by the line segment OP
Final velocity, v can be derived from velocity at point N or by the line segment NR
Also, NQ = NR – PO = v – u
Time interval, t is represented by OR, where OR = PQ = MN
- Deriving the Equation for Velocity – Time Relation
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- Deriving Equation for Position – Time Relation
We know that, distance travelled by an object = Area under the graph
So, Distance travelled = Area of OPNR = Area of rectangle OPQR + Area of triangle PQN
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- Deriving the Equation for Position – Velocity Relation
We know that, distance travelled by an object = area under the graph
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Also, we know that, (v – u)/ a = t [equation 2]
On equating equations 1 and 2, we get,
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Uniform Circular Motion – When an object travels in a circular path at a uniform speed the object is said to have a uniform circular motion.
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