Equations of Motion Derivation

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🎯 Part 1: Understanding Motion Variables

1. Match each variable to its correct definition by writing the letter in the circle:

A. Final velocity

B. Displacement

C. Time

D. Initial velocity

E. Acceleration

2. Which equation represents the definition of acceleration?

a = v + u

a = (v - u)/t

a = v × t

a = s/t

3. What is the formula for average velocity when acceleration is constant?

(u + v)/2

u + v

v - u

u × v

📝 Part 2: Equation Derivation Steps

4. Complete the derivation of the first equation of motion:

Starting with: a = (v - u)/t

Multiply both sides by t: at = _____________

Add u to both sides: u + at = _____________

Therefore: v = _____________

5. For the second equation of motion, we use s = average velocity × time.

If average velocity = (u + v)/2 and we substitute v = u + at:

Complete the algebra to show that s = ut + ½at²

6. Explain in your own words why we can use average velocity to find displacement when acceleration is constant:

🚀 Part 3: Real-World Applications

7. A car accelerates from rest at 3.0 ft/s². After 4.0 seconds, what is its velocity?

Given: u = _____ ft/s, a = _____ ft/s², t = _____ s

Equation to use: _____________

Answer: v = _____ ft/s

8. A ball is dropped from a 64-foot building. Using a = 32 ft/s², how long does it take to hit the ground?

Given: u = _____ ft/s, s = _____ ft, a = _____ ft/s²

Equation to use: _____________

Answer: t = _____ seconds

9. Extension Challenge: A rocket accelerates upward at 15 ft/s² for 8 seconds, then the engine cuts off. What is the maximum height it reaches? (Hint: You'll need two calculations!)

10. Reflection: Write one "I can..." statement describing what you learned about motion equations today:

Equations of Motion Derivation

Equations of Motion Derivation

🎯 Part 1: Understanding Motion Variables

📝 Part 2: Equation Derivation Steps

🚀 Part 3: Real-World Applications

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