Time and Distance

Rumman Ansari   Software Engineer   2024-07-28 09:03:18   52  Share
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Table of Content:

Time and Distance Formulas

Basic Formulas

Speed

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Distance

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Time

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Conversions

Speed in km/hr to m/s

\[ \text{Speed (m/s)} = \text{Speed (km/hr)} \times \frac{5}{18} \]

Speed in m/s to km/hr

\[ \text{Speed (km/hr)} = \text{Speed (m/s)} \times \frac{18}{5} \]

Relative Speed

Same Direction

\[ \text{Relative Speed} = \text{Speed}_1 - \text{Speed}_2 \]

Opposite Direction

\[ \text{Relative Speed} = \text{Speed}_1 + \text{Speed}_2 \]

Time to Meet

Time to Meet (Same Direction)

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Time to Meet (Opposite Direction)

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Average Speed

When the same distance is traveled at different speeds:

\[ \text{Average Speed} = \frac{2 \times \text{Speed}_1 \times \text{Speed}_2}{\text{Speed}_1 + \text{Speed}_2} \]

Examples

Example 1: Finding Speed

\[ \text{If a car travels 150 km in 3 hours, what is its speed?} \] \[ \text{Speed} = \frac{150 \text{ km}}{3 \text{ hours}} = 50 \text{ km/hr} \]

Example 2: Finding Time

\[ \text{If a person walks at a speed of 5 km/hr for 10 km, how long does it take?} \] \[ \text{Time} = \frac{10 \text{ km}}{5 \text{ km/hr}} = 2 \text{ hours} \]
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