Study sheet: Motion and Equations of Motion

📋 Course Outline

1. Rest, Motion, and Relativity
2. Types of Motion
3. Distance and Displacement
4. Speed and Velocity
5. Acceleration and Quantities
6. Equations of Uniform Motion
7. Motion Under Gravity
8. Historical Explanation of Gravity

📖 1. Rest, Motion, and Relativity

🔑 Key Concepts & Definitions

• Rest : the state in which an object does not change its position relative to its surroundings
• Motion : the state in which an object changes its position relative to its surroundings
• Relative motion : the motion of an object described with respect to another object or observer

📝 Essential Points

• A passenger in a moving train is at rest relative to other passengers but in motion relative to a person standing outside.

💡 Memory Hook

Rest for one observer can be motion for another.

📖 2. Types of Motion

🔑 Key Concepts & Definitions

• Translatory motion : occurs when every point of an object moves the same distance in a given time
• Linear motion : the motion of an object along a straight path
• Rotatory motion : Rotatory motion occurs when an object rotates or spins about its own axis, as a fan does.
• Circular motion : Circular motion is the motion of an object along a circular path, such as the motion of Earth around the Sun.
• Random motion : Random motion is motion that has no definite shape or pattern, such as the motion of air particles or water molecules.
• Vibratory motion : the to-and-fro motion of an object about its mean position

💡 Memory Hook

TRV: Translatory, Rotatory, Vibratory.

📖 3. Distance and Displacement

🔑 Key Concepts & Definitions

• Distance : the total length between two points or the total path covered by a body without direction
• Displacement : the shortest directed distance between an object's initial and final positions

★ Must-know

• Distance is a scalar quantity measured in metres in the SI system and can be positive.

• Displacement is a vector quantity measured in metres in the SI system and can be positive, negative, or zero.

Further detail

• If an object travels 3 km east and then 4 km west, its displacement from the initial position is 1 km west.

💡 Memory Hook

Distance measures total path, whereas displacement measures directed shortest separation.

📖 4. Speed and Velocity

🔑 Key Concepts & Definitions

• Speed : the rate of change of distance or the distance covered by a body per unit time
• Velocity : the rate of change of displacement or displacement covered per unit time in a particular direction

★ Must-know

📐 Formula — Speed is calculated by $v = \frac{s}{t}$ and has the SI unit m/s.

📐 Formula — Velocity is calculated by $\vec{v} = \frac{\Delta \vec{s}}{\Delta t}$ and has the SI unit m/s.

Further detail

📌 Uniform speed means covering equal distances in equal intervals of time, whereas uniform velocity means covering equal displacements in equal intervals of time.

💡 Memory Hook

Speed uses distance; velocity uses displacement and direction.

📖 5. Acceleration and Quantities

🔑 Key Concepts & Definitions

• Acceleration : the rate of change of velocity with respect to time
• Scalar quantity : A scalar quantity has magnitude and a unit but no direction, such as distance, speed, mass, length, and density.
• Vector quantity : A vector quantity has magnitude, a unit, and direction, such as force, velocity, displacement, acceleration, momentum, and torque.

★ Must-know

📐 Formula — Acceleration is calculated by $\vec{a} = \frac{\Delta \vec{v}}{\Delta t} = \frac{\vec{v}_f - \vec{v}_i}{t_2-t_1}$.

Further detail

• If velocity changes from 10 m/s to 20 m/s in 5 seconds, the acceleration is 2 m/s².

💡 Memory Hook

A change in velocity over time produces acceleration.

📖 6. Equations of Uniform Motion

★ Must-know

📌 Newton's equations of motion apply when acceleration is uniform. — Issac Newton

📐 Formula — The first equation of motion is $v_f = v_i + at$, where acceleration is $a = \frac{\Delta v}{\Delta t}$ and $\Delta v = v_f-v_i$. — Issac Newton

📐 Formula — The second equation of motion is $s = v_i t + \frac{1}{2}at^2$. — Issac Newton

📐 Formula — The third equation of motion is $v_f^2 = v_i^2 + 2as$. — Issac Newton

Further detail

• The third equation is derived by squaring the first equation, expanding with $(a+b)^2=a^2+2ab+b^2$, and substituting the displacement relation. — Issac Newton

💡 Memory Hook

Velocity first, displacement second, velocity-distance third.

📖 7. Motion Under Gravity

🔑 Key Concepts & Definitions

• Acceleration due to gravity : the acceleration produced in a body by Earth's gravity
• Motion under gravity : motion produced in a body only by Earth's gravitational force

★ Must-know

📌 For an object moving upward, gravity is taken as negative because the upward motion is opposite to the gravitational force.

Further detail

• A body thrown upward at 50 m/s reaches a maximum height of 127.55 m when the acceleration is -9.8 m/s² and the final velocity is zero.

• A ball dropped from 50 m with initial velocity zero reaches the ground at approximately 31.62 m/s when g is 10 m/s².

💡 Memory Hook

Earth's gravitational force causes downward acceleration.

📖 8. Historical Explanation of Gravity

★ Must-know

• Aristotle was a Greek philosopher who stated that heavier objects fall first and that falling speed is directly proportional to an object's weight.

Further detail

• Aristotle did not give the concept of acceleration but discussed speed in relation to weight.

• A feather and a stone dropped together in an air-filled glass tube illustrate the comparison of falling objects described in the gravity discussion.

💡 Memory Hook

Aristotle linked falling speed to weight, not acceleration.

📊 Synthesis Tables

Distance and Displacement

Quantity	Nature	Direction	Possible values
Distance	Scalar	No direction	Positive
Displacement	Vector	Has direction	Positive, negative, or zero

Speed and Velocity

Quantity	Definition	Nature	Formula
Speed	Rate of change of distance	Scalar	$v=s/t$
Velocity	Rate of change of displacement	Vector	$\vec{v}=\Delta\vec{s}/\Delta t$