Motion Short Notes | Class 9
Introduction
Motion is the change in position of an object with respect to time. It is a very common phenomenon in our daily life, e.g., a car on the road, a walking person, or a rolling ball.
→Types of Motion
- Rectilinear Motion: Motion in a straight line. For example, a car on a straight road.
- Circular Motion: Motion in a circular path. For example, the motion of the Earth around the Sun.
- Oscillatory Motion: Motion that takes place repeatedly in a regular cycle. For example, the motion of a pendulum.
- Scalar quantity :Scalars are physical quantities that have only magnitude (size or amount) and no direction.
- Vector Quantity: Vectors are physical quantities that have both magnitude and direction.
Distance and Displacement
Distance
- Definition: Distance is the total length of the path traveled by an object, regardless of direction.
- Depends on the path covered
- Scalar (only magnitude).
- Always positive.
- Nature: It is a scalar quantity, i.e., it has only magnitude and no direction.
- Example: If you go around a park and travel 500 meters, the distance is 500 meters regardless of the path covered.
Displacement
- Definition: Displacement is the shortest distance from the initial to the final position of an object, along with the direction.
- Depends only on the initial and final positions.
- Vector (magnitude and direction)
- Can be positive, negative, or zero.
- Nature: It is a vector quantity, i.e., it has both magnitude and direction.
- Example: If you go around a park and travel 500 meters and reach back to the initial position, your displacement is 0 meters since your initial and final positions are the same.
Uniform and Non-Uniform Motion
Uniform Motion
- Uniform motion is when an object covers equal distances in equal time intervals.
- The speed is constant during the motion.
- The object generally travels in a straight line.
- Because the speed is constant, the acceleration is zero.
- Examples : A car moving at a constant speed of 60 km/h on a straight road.
The hands of a clock traveling at a constant speed.
Non-Uniform Motion
- Non-uniform motion is when an object covers unequal distances in equal time intervals.
- The speed of the object is not constant during motion
- The path may be non-straight
- The object accelerates or decelerates
- Example: A car accelerating or decelerating as it travels.
→Two Types of non-uniform motion
1. Accelerated Motion
- Definition: When the speed of an object increases with time.
- Example: A car accelerating as it moves away from a traffic light.
2. Decelerated Motion
- Definition: When the speed of an object decreases with time.
- Example: A car slowing down as it approaches a stop sign.
Speed
Speed: Speed is the distance covered by an object in one unit of time. It is a scalar quantity, i.e., it has only magnitude and no direction.
Formula: The formula for speed is:
Speed=Time/Distance
where distance is the complete length of the path covered by the object, and time is the time to cover that distance.
__Types of Speed__
1. Uniform Speed:
- When an object covers equal distances in equal time intervals, it is said to be traveling with uniform speed.
- Example: A car traveling at a constant speed of 60 km/h.
2. Non-Uniform Speed
- When an object travels unequal distances in equal time intervals, it is said to be moving with non-uniform speed.
- Example: A car accelerating or decelerating while traveling.
Velocity
Velocity: Velocity is the rate of change of displacement of an object. Velocity is a vector quantity, i.e., it has both magnitude and direction.
Formula: The formula for velocity is:
Velocity=Time/Displacement
where displacement is the shortest distance between the initial and final position of the object, and time is the time taken to travel that distance.
Acceleration
- Acceleration: Acceleration is the rate of change of velocity of an object with respect to time. Acceleration is a vector quantity, i.e., it has both magnitude and direction.
- Formula: The formula for acceleration is:
- Acceleration=Time Taken Change in Velocity=tv−u
where:
- ( v ) = Final velocity
- ( u ) = Initial velocity
- ( t ) = Time taken for the change in velocity
Units of Acceleration
- The SI unit of acceleration is meters per second squared (m/s²).
Graphical Representation of Motion
1. Distance-Time Graph
- Uniform Motion: The distance-time graph of an object moving with uniform speed is a straight line. The slope of the line is the speed.
- Example: A car traveling with a constant speed of 60 km/h will have a straight-line graph.
- Non-Uniform Motion: The distance-time graph of an object moving with non-uniform speed is a curved line.
- Example: A car accelerating or decelerating will have a curved graph.
2. Velocity-Time Graph
- Uniform Velocity: The velocity-time graph of an object moving with uniform velocity is a straight line parallel to the time axis.
- Example: A car traveling with a constant velocity of 60 km/h east.
- Uniform Acceleration: For an object with uniform acceleration, the velocity-time graph is a straight line with constant slope.
- Example: A car uniformly accelerating.
- Non-Uniform Acceleration: For an object with non-uniform acceleration, the velocity-time graph is a curved line.
- Example: A car accelerating non-uniformly.
3. Acceleration-Time Graph
- Constant Acceleration: For an object with constant acceleration, the acceleration-time graph is a straight line parallel to the time axis.
- Example: A car uniformly accelerating at 2 m/s².
- Variable Acceleration: For an object with variable acceleration, the acceleration-time graph is a curved line.
- Example: A car with variable acceleration.
Key Points
- Slope of Distance-Time Graph: Represents speed.
- Slope of Velocity-Time Graph: Represents acceleration.
- Area under Velocity-Time Graph: Represents displacement.
- Area under Acceleration-Time Graph: Represents change in velocity.
Equation of Motion by Graphical Method
1. First Equation: v=u+atv=u+at
- Where v = final velocity, u = initial velocity, aa = acceleration, tt = time.
2. Second Equation: s=ut+1/2at^2
- where s = displacement
3. Third Equation: v^2=u^2+2as
Graphical Representation:
1. Velocity-Time Graph:
- To find displacement (ss), calculate the area under the curve:
- For rectangles and triangles, using Area=base×heightArea=base×height.
2. Analyzing Relationships:
- From the nature of the graphs (linearity, curves), deduce whether the motion is uniform or accelerated.
Example Analysis:
- If a velocity-time graph shows a straight upward line:
- The object is uniformly accelerating.
- The slope will give acceleration.
- Use area calculation to find displacement in the time interval.
Uniform Circular Motion
Uniform circular motion is the motion of an object that travels in a circular path at a constant speed.