ICSE Physics,class 9, Equations of motion

Derivation of Three Equations of Motion

🌈 Derivation of Three Equations of Motion

🔴 First Equation
v = u + at

🟠 Second Equation
s = ut + 1/2 at²

🟡 Third Equation
v² = u² + 2as

🟢 Symbols
u = Initial velocity
v = Final velocity

🔵 More Symbols
a = Acceleration
t = Time
s = Displacement

🟣 Condition
Applicable only for uniform acceleration.

⚫ Importance
Used to solve motion numericals.

🎯 Learning Objectives

• Understand equations of motion.
• Learn derivation step by step.
• Apply equations in numerical problems.

🧩 Competencies

• Conceptual Understanding
• Analytical Thinking
• Logical Reasoning
• Numerical Skills

📊 Learning Outcomes

• Derives all three equations correctly.
• Identifies physical quantities properly.
• Uses equations in solving problems.

📌 Evidence

• Correct derivation steps
• MCQ performance
• Numerical problem solving

📘 Derivation of First Equation of Motion

Acceleration = Change in velocity / Time taken

a = (v - u)/t

at = v - u

v = u + at

📘 Derivation of Second Equation of Motion

Displacement = Average velocity × Time

s = [(u + v)/2] × t

Using first equation:
v = u + at

s = [(u + u + at)/2] × t

s = [(2u + at)/2] × t

s = ut + 1/2 at²

s = ut + 1/2 at²

📘 Derivation of Third Equation of Motion

From first equation:
v = u + at

a = (v-u)/t

t = (v-u)/a

From second equation:
s = [(u + v)/2] × t

Substitute value of t:

s = [(u + v)/2] × [(v-u)/a]

2as = (u + v)(v - u)

2as = v² - u²

v² = u² + 2as

📝 Quiz

1. First equation of motion is:

v = u + at s = ut v² = u²

2. Symbol ‘a’ represents:

Area Acceleration Amplitude

3. Third equation of motion is:

s = ut v² = u² + 2as a = vt

4. Equations of motion are valid for:

Uniform acceleration Circular motion Random motion

5. Symbol ‘u’ represents:

Final velocity Initial velocity Uniform speed

🧠 HOTS Questions

1. Why are equations of motion useful in physics?

They help calculate displacement, velocity and acceleration easily.

2. Why can these equations not be used for non-uniform acceleration?

Because acceleration changes continuously in non-uniform motion.

3. Which equation is useful when time is not given?

v² = u² + 2as

4. Why is acceleration important in motion?

Acceleration changes the velocity of a moving object.

5. Why is velocity a vector quantity?

Because velocity has both magnitude and direction.