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Unit Conversion (m/s ↔ km/h)

Introduction

In speed-related questions, values are often given in different units - meters per second (m/s) or kilometers per hour (km/h). Understanding how to convert between these two is essential because mixing units can lead to incorrect answers even if your calculation is right.

This pattern helps you quickly switch between m/s and km/h so your formulas stay consistent and accurate.

Pattern: Unit Conversion (m/s ↔ km/h)

Pattern

The key concept is converting between meters per second and kilometers per hour using a constant multiplier.

  • To convert km/h → m/s: multiply by 5/18.
  • To convert m/s → km/h: multiply by 18/5.

This is because 1 km = 1000 m and 1 hour = 3600 seconds, and 1000 ÷ 3600 = 5/18.

Step-by-Step Example

Question

Convert a speed of 72 km/h into m/s.

Solution

  1. Step 1: Identify Given Value

    Speed = 72 km/h. We need to convert this into m/s.

  2. Step 2: Apply Conversion Formula

    1 km/h = 5/18 m/s → So, multiply 72 by 5/18.

  3. Step 3: Calculate

    72 × (5/18) = 72 ÷ 18 × 5 = 4 × 5 = 20 m/s.

  4. Final Answer:

    72 km/h = 20 m/s.

  5. Quick Check:

    Convert back: 20 × (18/5) = 72 km/h ✅ (verified).

Quick Variations

1. Converting walking/running speeds between km/h and m/s.

2. Using converted units inside distance-time formulas (e.g., train problems with meters).

3. Comparing two moving objects given in different units.

4. Practical use in physics and mechanics problems involving acceleration or motion.

Trick to Always Use

  • Step 1: Remember the fixed multipliers - 5/18 and 18/5.
  • Step 2: For km/h → m/s → multiply by 5/18.
  • Step 3: For m/s → km/h → multiply by 18/5.
  • Step 4: Always check if units in the formula (D = S × T) match - convert if not.

Summary

Summary

  • 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h.
  • Always convert all speeds into the same unit before solving.
  • Quick memory tip: “Multiply by 5/18 to go smaller (to m/s)” and “Multiply by 18/5 to go bigger (to km/h)”.
  • Cross-verify by converting back - the two results should match.

Practice

(1/5)
1. Convert 36 km/h into m/s.
easy
A. 10 m/s
B. 8 m/s
C. 9 m/s
D. 11 m/s

Solution

  1. Step 1: Identify Given Value

    Speed = 36 km/h.

  2. Step 2: Apply Conversion Formula

    To convert km/h → m/s, multiply by 5/18.

  3. Step 3: Calculate

    36 × 5/18 = (36 ÷ 18) × 5 = 2 × 5 = 10 m/s.

  4. Final Answer:

    36 km/h = 10 m/s → Option A.

  5. Quick Check:

    Convert back: 10 × 18/5 = 36 km/h ✅
Hint: Multiply km/h by 5/18 to get m/s.
Common Mistakes: Using 18/5 instead of 5/18 when converting to m/s.
2. Convert 20 m/s into km/h.
easy
A. 60 km/h
B. 70 km/h
C. 72 km/h
D. 75 km/h

Solution

  1. Step 1: Identify Given Value

    Speed = 20 m/s.

  2. Step 2: Apply Conversion Formula

    To convert m/s → km/h, multiply by 18/5.

  3. Step 3: Calculate

    20 × 18/5 = (20 ÷ 5) × 18 = 4 × 18 = 72 km/h.

  4. Final Answer:

    20 m/s = 72 km/h → Option C.

  5. Quick Check:

    72 × 5/18 = 20 m/s ✅
Hint: Multiply m/s by 18/5 to convert to km/h.
Common Mistakes: Dividing by 18/5 instead of multiplying.
3. Convert 90 km/h into m/s.
easy
A. 24 m/s
B. 25 m/s
C. 26 m/s
D. 27 m/s

Solution

  1. Step 1: Identify Given Value

    Speed = 90 km/h.

  2. Step 2: Apply Conversion Formula

    To convert km/h → m/s, multiply by 5/18.

  3. Step 3: Calculate

    90 × 5/18 = (90 ÷ 18) × 5 = 5 × 5 = 25 m/s.

  4. Final Answer:

    90 km/h = 25 m/s → Option B.

  5. Quick Check:

    25 × 18/5 = 90 km/h ✅
Hint: Use × 5/18 for km/h → m/s conversions.
Common Mistakes: Multiplying by 18/5 instead of 5/18.
4. Convert 15 m/s into km/h.
medium
A. 52 km/h
B. 53 km/h
C. 55 km/h
D. 54 km/h

Solution

  1. Step 1: Identify Given Value

    Speed = 15 m/s.

  2. Step 2: Apply Conversion Formula

    To convert m/s → km/h, multiply by 18/5.

  3. Step 3: Calculate

    15 × 18/5 = (15 ÷ 5) × 18 = 3 × 18 = 54 km/h.

  4. Final Answer:

    15 m/s = 54 km/h → Option D.

  5. Quick Check:

    54 × 5/18 = 15 m/s ✅
Hint: Multiply m/s by 18/5 to convert to km/h.
Common Mistakes: Using 5/18 instead of 18/5 for m/s → km/h.
5. A train moves at a speed of 108 km/h. Express this in m/s.
medium
A. 30 m/s
B. 29 m/s
C. 28 m/s
D. 31 m/s

Solution

  1. Step 1: Identify Given Value

    Speed = 108 km/h.

  2. Step 2: Apply Conversion Formula

    To convert km/h → m/s, multiply by 5/18.

  3. Step 3: Calculate

    108 × 5/18 = (108 ÷ 18) × 5 = 6 × 5 = 30 m/s.

  4. Final Answer:

    108 km/h = 30 m/s → Option A.

  5. Quick Check:

    30 × 18/5 = 108 km/h ✅
Hint: Multiply km/h by 5/18 to get m/s.
Common Mistakes: Using 18/5 for km/h → m/s conversion.

Mock Test

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