Physics - Mechanics and Properties of Matter - How to Solve: Motion in a Straight Line (Equations of Motion, Graphs) – NEET UG Physics

How to Solve: Motion in a Straight Line (Equations of Motion, Graphs) – NEET UG Physics

Complete Guide

Introduction

"Mastering motion in a straight line unlocks 3–5 direct NEET questions—worth 12–20 marks—plus the foundation for projectile motion, circular motion, and even rotational dynamics. Miss this, and you’re leaving easy marks on the table."

WHAT YOU NEED TO KNOW FIRST

1. Displacement vs. Distance – Displacement is a vector (direction matters); distance is scalar.
2. Average Speed vs. Average Velocity – Speed = total distance / time; velocity = displacement / time.
3. Acceleration – Rate of change of velocity (vector). Units: m/s².

KEY TERMS & FORMULAS

Key Terms

• Initial velocity (u) – Velocity at time t = 0.
• Final velocity (v) – Velocity at time t.
• Acceleration (a) – Rate of change of velocity (constant in these problems).
• Displacement (s) – Change in position (vector).
• Time (t) – Duration of motion.

Equations of Motion (MEMORISE THIS)

1. First Equation (Velocity-Time Relation)
   [ v = u + at ]
2. v = final velocity (m/s)
3. u = initial velocity (m/s)
4. a = acceleration (m/s²)

5. t = time (s)

6. Second Equation (Displacement-Time Relation)
   [ s = ut + \frac{1}{2}at^2 ]

7. s = displacement (m)

8. Third Equation (Velocity-Displacement Relation)
   [ v^2 = u^2 + 2as ]

9. Displacement from Average Velocity (MEMORISE THIS)
   [ s = \left( \frac{u + v}{2} \right) t ]

Graphs (MEMORISE THIS)

• v-t Graph:
• Slope = acceleration (a = Δv/Δt)
• Area under graph = displacement (s = area)
• s-t Graph:
• Slope = velocity (v = Δs/Δt)

STEP-BY-STEP METHOD

Step 1: Read the Problem Carefully

• Underline given values (u, v, a, s, t).
• Circle what is asked (e.g., "Find displacement" or "Find time").

Step 2: Choose the Right Equation

• Missing v? → Use ( s = ut + \frac{1}{2}at^2 )
• Missing s? → Use ( v = u + at )
• Missing t? → Use ( v^2 = u^2 + 2as )
• Missing a? → Use ( s = \left( \frac{u + v}{2} \right) t )

Step 3: Plug in Values & Solve

• Write the equation.
• Substitute known values.
• Solve for the unknown.

Step 4: Check Units & Signs

• Units: All must be in m, s, m/s, m/s².
• Signs:
• a is positive if speeding up in the same direction as u.
• a is negative if slowing down (deceleration).
• s is positive if in the same direction as u; negative if opposite.

Step 5: Verify with Graphs (If Needed)

• Sketch a v-t graph to confirm displacement (area under curve).
• Sketch an s-t graph to confirm velocity (slope).

WORKED EXAMPLES

Example 1 – Basic (Missing v)

Problem: A car starts from rest and accelerates at 2 m/s² for 5 s. Find its final velocity.

Solution: 1. Given:
- u = 0 m/s (starts from rest)
- a = 2 m/s²
- t = 5 s
- v = ?

1. Equation: ( v = u + at )

2. Substitute:
   [ v = 0 + (2)(5) ]
   [ v = 10 \, \text{m/s} ]

What we did and why: - Used the first equation because v was missing. - Confirmed units (m/s², s → m/s).

Example 2 – Medium (Missing s)

Problem: A bike moving at 10 m/s brakes with deceleration 2 m/s². How far does it travel before stopping?

Solution: 1. Given:
- u = 10 m/s
- v = 0 m/s (stops)
- a = -2 m/s² (deceleration)
- s = ?

1. Equation: ( v^2 = u^2 + 2as )

2. Substitute:
   [ 0 = (10)^2 + 2(-2)(s) ]
   [ 0 = 100 - 4s ]
   [ 4s = 100 ]
   [ s = 25 \, \text{m} ]

What we did and why: - Used the third equation because t was missing. - Made a negative (deceleration). - Confirmed displacement is positive (same direction as u).

Example 3 – Exam-Style (Disguised Problem)

Problem: A train accelerates from 18 km/h to 72 km/h in 10 s. Find the distance covered in this time.

Solution: 1. Convert units:
- u = 18 km/h = ( 18 \times \frac{1000}{3600} = 5 \, \text{m/s} )
- v = 72 km/h = ( 72 \times \frac{1000}{3600} = 20 \, \text{m/s} )
- t = 10 s

1. Find a:
   [ v = u + at ]
   [ 20 = 5 + a(10) ]
   [ a = 1.5 \, \text{m/s²} ]

2. Find s:
   [ s = ut + \frac{1}{2}at^2 ]
   [ s = (5)(10) + \frac{1}{2}(1.5)(10)^2 ]
   [ s = 50 + 75 = 125 \, \text{m} ]

What we did and why: - Converted km/h to m/s first (common NEET trap). - Found a first because s required it. - Used the second equation for displacement.

COMMON MISTAKES

1. MISTAKE: Forgetting to convert km/h to m/s.
   WHY IT HAPPENS: NEET often gives speed in km/h but expects m/s.
   CORRECT APPROACH: Always convert to m/s first.

2. MISTAKE: Using the wrong sign for acceleration.
   WHY IT HAPPENS: Confusing deceleration with negative acceleration.
   CORRECT APPROACH: If slowing down, a is negative.

3. MISTAKE: Mixing up displacement and distance.
   WHY IT HAPPENS: Ignoring direction (vector vs. scalar).
   CORRECT APPROACH: Displacement is net change in position; distance is total path length.

4. MISTAKE: Using the wrong equation.
   WHY IT HAPPENS: Not checking which variable is missing.
   CORRECT APPROACH: Pick the equation that excludes the unknown.

5. MISTAKE: Misinterpreting graphs.
   WHY IT HAPPENS: Confusing slope and area.
   CORRECT APPROACH:

6. v-t graph: Slope = a, area = s.
7. s-t graph: Slope = v.

EXAM TRAPS

1. TRAP: Giving acceleration in km/h² instead of m/s².
   HOW TO SPOT IT: Units are not m/s².
   HOW TO AVOID IT: Convert to m/s² first.

2. TRAP: Asking for "distance" but expecting "displacement."
   HOW TO SPOT IT: The problem mentions "net change" or "position."
   HOW TO AVOID IT: Read carefully—displacement is a vector.

3. TRAP: Hiding deceleration as "retardation."
   HOW TO SPOT IT: The problem says "retards" or "slows down."
   HOW TO AVOID IT: Treat retardation as negative acceleration.

1-MINUTE RECAP (Night Before Exam)

"Listen up—this is your 60-second crash course for NEET motion problems. First, memorise the three equations: 1. ( v = u + at ) (missing s) 2. ( s = ut + \frac{1}{2}at^2 ) (missing v) 3. ( v^2 = u^2 + 2as ) (missing t)

Always convert km/h to m/s—divide by 3.6. Watch signs: acceleration is negative if slowing down. For graphs, remember: - v-t graph: Slope = acceleration, area = displacement. - s-t graph: Slope = velocity.

If stuck, sketch the graph—it’ll save you. And if a problem gives you km/h, convert first. You’ve got this—go ace those 12 marks!