Motion - Notes

📘 Motion – SSC Conceptual Breakdown

🧮 Formulas

• v = u + at – Final velocity (v)
• s = ut + ½at² – Displacement under uniform acceleration
• v² = u² + 2as – Relation between velocity and displacement (no time)
• s = vt - ½at² – Displacement (final velocity known)
• s = (u + v)/2 × t – Displacement using average velocity
• a = (v - u)/t – Acceleration formula
• v_avg = 2v₁v₂ / (v₁ + v₂) – Average speed for equal distance cases
• Speed = Distance / Time – Basic speed formula
• Relative Speed = v₁ ± v₂ – For approaching or receding objects
• g = 9.8 m/s² – Acceleration due to gravity (use 10 for SSC)

📚 Types of Problems / Models

1. Uniform Motion – Constant speed, no acceleration.
2. Uniformly Accelerated Motion – Constant acceleration (most SSC problems).
3. Relative Motion – Two bodies moving in same/opposite directions.
4. Train-Based Problems – Passing a pole, platform, or another train.
5. Boat and Stream – Effective speed upstream/downstream.
6. Circular Motion – Number of revolutions, speed, time.
7. Free Fall / Vertical Motion – Under gravity alone.
8. Average Speed – Especially for different speeds over equal distances.

🚀 Tricks & Shortcuts

• Average speed for equal distances: v_avg = 2v₁v₂ / (v₁ + v₂)
• Train passing a pole: Time = Train Length / Speed
• Train passing platform: Time = (Train + Platform Length) / Speed
• Relative Speed:
  • Same direction: v₁ - v₂
  • Opposite direction: v₁ + v₂

💡 Real-World Examples

• Speed limits on roads apply distance-time concepts.
• Metro acceleration/deceleration use uniformly accelerated motion.
• Boats use stream-based motion to calculate effective speeds.
• Airplanes use relative motion for tracking and interception.
• Roller coasters simulate free fall conditions for thrill rides.

1️⃣ Uniform Motion

Problem: A cyclist travels 90 km in 3 hours. What is the speed?

Solution:
Using Speed = Distance / Time
Speed = 90 / 3 = 30 km/h

2️⃣ Uniformly Accelerated Motion

Problem: A car starts from rest and accelerates at 2 m/s² for 8 seconds. Find the distance.

Solution:
Given: u = 0, a = 2, t = 8
Use s = ut + ½at²
s = 0 + ½ × 2 × 64 = 64 m

3️⃣ Relative Motion

Problem: Two trains move in the same direction at 70 km/h and 50 km/h. The faster train is 210 m long. How long to pass the slower one?

Solution:
Relative speed = 20 km/h = 20×(5/18) = 5.56 m/s
Time = 210 / 5.56 ≈ 37.8 sec

4️⃣ Train-Based Problem

Problem: A 150 m train passes a 90 m platform in 12 seconds. Find speed.

Solution:
Distance = 150 + 90 = 240 m, Time = 12 s
Speed = 240 / 12 = 20 m/s = 72 km/h

5️⃣ Boat and Stream

Problem: Boat speed in still water = 10 km/h, stream speed = 2 km/h. Find time to go 24 km downstream.

Solution:
Downstream speed = 10 + 2 = 12 km/h
Time = 24 / 12 = 2 hours

6️⃣ Free Fall

Problem: A stone is dropped from 80 m. How long will it take to fall? (g = 10 m/s²)

Solution:
s = ½gt² → 80 = 5t² → t² = 16 → t = 4 sec

7️⃣ Average Speed

Problem: A person goes to a city at 60 km/h and returns at 40 km/h. Find average speed.

Solution:
v_avg = 2 × 60 × 40 / (60 + 40) = 4800 / 100 = 48 km/h

⚠️ Common Mistakes

❌ Mixing units: Always convert km/h to m/s using 1 km/h = 5/18 m/s

❌ Not adding train + platform: Always include both lengths for total distance.

❌ Misusing average speed formula: Only use 2v₁v₂ / (v₁ + v₂) for equal distances.

❌ Sign confusion in relative motion: Use + for opposite, − for same direction.

❌ Ignoring 'starts from rest': Always check if u = 0 is given.

❌ Using g = 9.8 instead of 10: For faster SSC calculations, prefer g = 10 m/s²