Speed, Time, and Distance

This summary provides a comprehensive, easy-to-understand guide to the Speed, Time, and Distance PDF, including definitions, key formulas, solved examples, a cheatsheet, practice questions with answers, and visual aids.

1. Core Concepts and Definitions

Key Relationship:

¹²³⁴⁵⁶

2. Unit Conversions Cheatsheet

Example: Convert 54 km/hr to m/s: $ 54 \times \frac{5}{18} = 15 $ m/s¹.

3. Key Formulas and Shortcuts

A. Basic Formulas

• Speed: $ Speed = \frac{Distance}{Time} $
• Distance: $ Distance = Speed \times Time $
• Time: $ Time = \frac{Distance}{Speed} $¹²³⁴⁵⁶

B. Average Speed

• If total distance = $ d_1 + d_2 + … $, total time = $ t_1 + t_2 + … $:

• If equal distances at speeds $ x $ and $ y $:

• If equal time at speeds $ x $ and $ y $:

¹²⁵⁶

C. Relative Speed

• Same Direction: $ Relative Speed = |x - y| $
• Opposite Direction: $ Relative Speed = x + y $
• For trains crossing each other:

where $ L_1, L_2 $ are lengths of the trains³.

D. Ratio of Speed/Time

• If speed ratio is $ a:b $, time ratio is $ b:a $¹⁴⁵.

4. Visuals and Graphics

A. Relationship Triangle

      Distance
      /      \
Speed ------- Time

• Cover any one to get the formula for the other two.

B. Speedometer Analogy

• Think of speed as what a speedometer shows: how fast you cover distance per unit time.

5. Solved Examples

Example 1: Unit Conversion

Q: Convert 20 m/s to km/hr. A: $ 20 \times \frac{18}{5} = 72 $ km/hr¹.

Example 2: Ratio of Times

Q: Speeds of three cars: 5:4:6. Find time ratio for same distance. A: Time ratio = $ 1/5 : 1/4 : 1/6 = 12 : 15 : 10 $¹.

Example 3: Average Speed (Different Speeds)

Q: A man travels 12 km at 4 km/hr, then 10 km at 5 km/hr. What is the average speed? A: Time = $ 12/4 + 10/5 = 3 + 2 = 5 $ hr Average speed = $ (12 + 10)/5 = 22/5 = 4.4 $ km/hr¹.

Example 4: Average Speed (Equal Distances)

Q: 50 km at 50 km/hr, return at 75 km/hr. Average speed? A: $ Average speed = \frac{2 \times 50 \times 75}{50 + 75} = 60 $ km/hr¹.

6. Practice Questions with Answers

1. Two people, Shaan (50 km/hr) and Rohan (30 km/hr), start from different places 710 km apart. Shaan starts 3 hours earlier. Where do they meet relative to N? Answer: 500 km from N¹.
2. Two cars depart from A (10 am, 80 km/hr) and B (1 pm, 50 km/hr), 370 km apart. When do they meet? Answer: 2:00 pm¹.
3. A man takes 5 hr 45 min to walk to a place and ride back. If riding both ways, he’d save 2 hours. Time to walk both ways? Answer: 7 hr 45 min¹.
4. A and B start together at 40 km/hr and 50 km/hr. A takes 15 min longer. What’s the journey distance? Answer: 50 km¹.
5. Cyclist covers 750 m in 2 min 30 sec. What is the speed in km/hr? Answer: 18 km/hr¹.
6. A Jackal takes 4 leaps for every 5 of a goat, but 3 Jackal leaps = 4 goat leaps. Compare speeds. Answer: 16:15¹.

7. Additional Tips and Tricks

• Always check units before applying formulas.
• For trains, boats, and races, use relative speed.
• For average speed, use correct formula based on whether distance or time is constant.
• For ratios, remember speed and time are inversely proportional for the same distance.

8. Quick Reference Table (Cheatsheet)

9. Summary

• Speed, time, and distance are fundamentally linked: knowing any two lets you find the third.
• Master unit conversions and always check units before solving.
• Practice with a variety of problems: straight-line motion, trains, races, boats, etc.
• Use the formulas and cheatsheet above for quick revision.

With these explanations, formulas, examples, cheatsheets, solved and practice questions, and visuals, you’ll be ready to solve any Speed, Time, and Distance problem in exams!