Motion Class 9 Notes Science Chapter 7

• In our daily lives, objects such as birds, fish, and cars can be either at rest or in motion.
• Motion is a change of position and can be described in terms of the distance moved or the displacement.
• Motion is noticed when an object's position changes over time.
• Sometimes, we can indirectly observe motion, such as when we see leaves moving and infer that air is blowing.
• The perception of motion can differ; for example, passengers in a moving bus see trees moving backwards, while people outside see both the bus and its passengers moving.

Motion

Describing Motion

To describe an object's motion, we use a reference point, or origin, as a fixed location. For example, if a school is 2 km north of a railway station, the railway station serves as the reference point. This origin helps us measure and describe the object's position in relation to it.

What is Motion?

A body is considered to be in motion when its position changes continuously in relation to a reference point. The motion of an object could be uniform or non-uniform, depending on whether its speed is constant or changing. Motion can take different forms based on the path an object travels:

• Circulatory motion/Circular motion: In a circular path.
• Linear motion: In a straight-line path.
• Oscillatory/Vibratory motion: A to and fro path with respect to the origin.Types of Motion

Motion Along a Straight Line

The simplest type of motion is along a straight line. Let's understand this with an example. Imagine an object moving along a straight path, starting from point O, which we use as the reference point.

Example Description

• Initial Motion: The object begins at point O and moves to point A via points C and B.
• Return Motion: The object then travels back from A to C through B.

Distance Covered

During its journey from O to A and back to B, the distance covered helps describe the overall motion of the object and locate its final position relative to its initial position at a given time:

• Distance from O to A: 60 km
• Distance from A to C: 25 km
• Total Distance from O to C = OA + AC = 60 km + 25 km = 85 km

Distance is a scalar quantity, meaning it has magnitude but no direction. On the other hand, displacement is a vector quantity, which needs both magnitude and direction.

• Scalar quantity: A physical quantity that has magnitude but no direction. Example: Distance, Speed.
• Vector quantity: A physical quantity that requires both magnitude and direction. Example: Displacement, Velocity.

Distance and Displacement

1. Distance

The actual length of the path travelled by an object from its starting point to its end point is known as distance.

• Distance is a scalar quantity, meaning it only has magnitude and no direction. For example, Ramesh travelled 65 km. (Distance can be measured using an odometer in vehicles.)

2. Displacement

The shortest path from an object's starting position to its ending position is called displacement.

• Displacement is a vector quantity, meaning it has both magnitude and direction. For instance, Ramesh travelled 65 km to the southwest from the Clock Tower.
• Displacement can be zero if the start and end points are the same.

Example of Zero Displacement

Example 1: A body travels in a semicircular path with a radius of 10 m, starting from point ‘A’ to point ‘B’. Calculate the distance and displacement.

Solution: Given, π = 3.14, R = 10 m. Distance = πR = 3.14 × 10 = 31.4 m

Displacement = 2 × R = 2 × 10 = 20 m

Example 2: A body travels 4 km north, then turns right and travels another 4 km before stopping. Calculate:

(i) total distance travelled,

(ii) total displacement.

Solution: Total distance = OA + AB = 4 km + 4 km = 8 km

Total displacement = OB

Uniform and Non-uniform Motion

1. Uniform Motion

• When a body travels equal distances in equal time intervals, it is said to be in uniform motion.

2. Non-uniform Motion

• In this type of motion, a body travels unequal distances in equal time intervals.
• There are two types of non-uniform motion:
  • Accelerated Motion: When a body speeds up over time.
  • De-accelerated Motion: When a body slows down over time.

Uniform Circular Motion

If an object moves in a circular path at a constant speed, this is called uniform circular motion.

Measuring the Rate of Motion

• The rate at which objects move can vary, and different objects can also move at the same rate.
• One way to measure the rate of motion of an object is to determine the distance it travels in a given time.
• This measure is known as speed.
• The distance travelled by an object per unit of time is termed speed, and its SI unit is metre per second (m/s).
• Other units for speed include centimetre per second (cm/s) and kilometre per hour (km/h).
• In uniform motion, the speed remains constant.
• In non-uniform motion, the speed changes throughout the object's movement.
• Average speed gives a single value of speed during the motion, calculated as:

Conversion Factor: To convert from km/h to m/s: 1000 m / (60 × 60) s = 5/18 m/s.

Example: What will be the speed of body in m/s and km/hr if it travels 40 km in 5 hrs?
Sol: Distance (s) = 40 km
Time (t)  = 5 hrs.
Speed (in km/hr) = Total distance/Total time = 40/5 = 8 km/hr
40 km = 40 × 1000 m = 40,000 m
5 hrs = 5 × 60 × 60 sec.
Speed (in m/s) = (40 × 1000)/(5×60 ×60) = 80/36 = 2.22 m/s

Speed with Direction

• The rate of motion of an object becomes more comprehensive when its direction is specified along with its speed. This combined measure is called velocity.
• Velocity is the speed of an object moving in a specific direction. It is defined as the displacement travelled by a body per unit of time: Velocity = Displacement / Time.
• The SI unit of velocity is m/s.
• Since velocity is a vector quantity, its value changes if either its magnitude or direction changes.
• It can be positive ( +ve), negative (-ve), or zero.
• For non-uniform motion in a straight line, average velocity is calculated similarly to average speed: Average velocity = Total displacement / Total time.
• For uniformly changing velocity, average velocity can be calculated as follows:
• Average Velocity (v_avg) = (Initial velocity + Final velocity) / 2 = (u + v) / 2 where u = initial velocity and v = final velocity.

Example: During the first half of a journey, a body travels at a speed of 40 km/h, and in the second half, it travels at 20 km/h. The average speed for a journey with equal distances but different speeds is given by:

Average speed = 2 * (v1 * v2) / (v1 + v2) where v1 and v2 are the different speeds.

Average Speed Calculation

Speed during the first half (v1): 40 km/hr

Speed during the second half (v2): 20 km/hr

To calculate average speed, we use the formula:

Average Speed = Total Distance / Total Time

Example 1: Average Speed Calculation

A car travels 20 km in the first hour, 40 km in the second hour, and 30 km in the third hour. Calculate the average speed of the vehicle.Solution:

• Distance travelled during 1st hour: 20 km
• Distance travelled during 2nd hour: 40 km
• Distance travelled during 3rd hour: 30 km

Total Distance = 20 km + 40 km + 30 km = 90 km

Total Time = 1 hr + 1 hr + 1 hr = 3 hr

Now, applying the formula:

Average Speed = Total Distance / Total Time

Average Speed = 90 km / 3 hr = 30 km/hr

Explanation of Average Speed

Average speed is defined as the total distance travelled divided by the total time taken. It provides a measure of how fast an object is moving over a specific period, regardless of variations in speed during that time.

Summary

The average speed of the car is 30 km/hr. This calculation demonstrates how to find average speed by considering total distance and total time, which is crucial for understanding motion in physics.

Rate of Change of Velocity

• Acceleration occurs in non-uniform motion and is defined as the rate at which velocity changes over time. This type of motion is referred to as accelerated motion. The formula for acceleration (a) is:
• a = Change in velocity / Time = (v - u) / t
  where v = final velocity, u = initial velocity.
• The acceleration is positive if it is in the same direction as the velocity and negative if it is in the opposite direction.
• The SI unit of acceleration is m s².

Example Calculation

A car's speed increases from 40 km/hr to 60 km/hr in 5 seconds. To calculate the acceleration:

• Initial velocity, u = 40 km/hr = (40 × 5) / 18 = 100 / 9 ≈ 11.11 m/s
• Final velocity, v = 60 km/hr = (60 × 5) / 18 = 150 / 9 ≈ 16.66 m/s
• Time, t = 5 seconds

Substituting into the formula:

• a = (v - u) / t = (16.66 - 11.11) / 5 = 5.55 / 5 = 1.11 m/s².

Furthermore, if an object moves in a straight line and its velocity changes by equal amounts in equal time intervals, the acceleration is considered uniform. An example of this is the motion of a freely falling body. On the other hand, if a car increases its speed by different amounts in equal time intervals, it has non-uniform acceleration.

Retardation/Deceleration

• Deceleration, also referred to as retardation, means the reduction in the speed of an object over time. It is a type of acceleration where the change in speed is negative.
• Acceleration measures how much an object's speed changes over time. It is calculated as: acceleration (a) = Change in speed / Time = (v - u) / t. If the final speed (v) is less than the initial speed (u), then the acceleration is negative (a < 0).
• The standard unit of acceleration is m/s².

Example: A car moving at an initial speed of 20 km/hr stops in 0.5 hours. What is its retardation?

• Final speed (v) = 0 km/hr
• Initial speed (u) = 20 km/hr
• Time (t) = 0.5 hrs
• Retardation (a) = (v - u) / t = (0 - 20) / 0.5 = -40 km/hr².

Summary of Key Concepts

• If an object moves in a straight line and its speed increases or decreases by the same amount in equal time periods, the acceleration is considered uniform.
• If the speed changes at varying rates, the object has non-uniform acceleration.

Graphical Representation of Motion

1. Distance-Time Graph (s/t graph)

• When an object travels equal distances in equal time intervals, it moves with uniform speed.
• The distance-time graph for uniform motion is a straight line, showing constant speed.
• A curved line indicates non-uniform motion, where speed changes over time.

2. Velocity-Time Graph (v/t graph)

• (i) For uniform motion, the height of the v/t graph remains unchanged, indicating zero acceleration.
• (ii) In uniformly accelerated motion, velocity increases equally in equal time intervals.
• (iii) In non-uniformly accelerated motion, acceleration varies, and the graph can have different shapes.
• (iv) The graph for uniformly decelerated motion shows a steady decrease in velocity over time.
• (v) For non-uniformly decelerated motion, acceleration changes over time, which is reflected in the graph.

Note: In the v/t graph, the area between any two time intervals, t2 - t1, represents the total displacement of the body. The area under the velocity-time graph and the time axis gives the magnitude of the displacement.

The total distance travelled by the body between t2 and t1 can be calculated as follows:

• Total distance = Area of triangle + Area of rectangle = ½ × (v2 – v1) × (t2 - t1) + v1 × (t2 - t1)

Activity: Plot the distance-time graph for accelerated motion based on the provided data and interpret the results.

Equations of Motion by Graphical Method

1. Definition of Equations of Motion

When an object moves in a straight line with a constant acceleration, we can connect its velocity, acceleration, and the distance travelled over a specific time using a group of equations called the equations of motion.

2. First Equation: v = u + at

Final velocity (v) = Initial velocity (u) + Acceleration (a) × Time (t)

Graphical Derivation: Imagine a body starting with an initial velocity u at point A, which changes to v at point B in t seconds. So, the final velocity is v.

• There will be an acceleration.
• a = Change in velocity / Change in Time
• a = (OB - OA) / (OC - 0) = (v - u) / (t - 0)
• Thus, a = (v - u) / t
• Therefore, v = u + at.

3. Second Equation: s = ut + ½ at²

Distance travelled by the object (s) = Area of rectangle ABCD + Area of triangle ADE

• s = OA × AD + ½ × AD × BD
• s = u × t + ½ × t × (v – u)
• s = ut + ½ × t × at
• Thus, s = ut + ½ at².

4. Third Equation: v² = u² + 2as

This equation connects the final velocity, initial velocity, acceleration, and distance travelled by the object.

5. Context of Variables

• u is the initial velocity,
• v is the final velocity,
• a is the acceleration,
• s is the distance travelled by the object in time t.

6. Graphical Representation of Motion

These equations can be derived visually, which is crucial for understanding how they apply.

Uniform Circular Motion

• If a body is moving in a circular path with constant speed, it is said to be in uniform circular motion. While the speed remains the same, the velocity (which is the direction of motion) changes at each point. For example, an athlete running along a circular track is demonstrating accelerated motion.