Speed and Distance Formulas

1. Speed Formula

$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

Speed is calculated as distance traveled divided by the time taken.

2. Distance Formula

$\mathrm{Distance}=\mathrm{Speed}\times \mathrm{Time}$

Distance is the product of speed and time.

3. Time Formula

$\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}$

Time is calculated as distance divided by speed.

4. Average Speed

$\mathrm{Average\; Speed}=\frac{\mathrm{Total\; Distance}}{\mathrm{Total\; Time}}$

Average speed is the total distance traveled divided by the total time taken.

5. Relative Speed

Case 1 (Same Direction):

$\mathrm{Relative\; Speed}=\mathrm{Speed}{1}_{}–\mathrm{Speed}{2}_{}$

Case 2 (Opposite Direction):

$\mathrm{Relative\; Speed}=\mathrm{Speed}{1}_{}+\mathrm{Speed}{2}_{}$

Relative speed depends on whether objects are moving in the same or opposite directions.

6. Unit Conversion

From km/h to m/s:

$\mathrm{Speed}\left(\mathrm{m/s}\right)=\mathrm{Speed}\left(\mathrm{km/h}\right)\times 5/18$

From m/s to km/h:

$\mathrm{Speed}\left(\mathrm{km/h}\right)=\mathrm{Speed}\left(\mathrm{m/s}\right)\times 18/5$

Use these formulas to convert speed between kilometers per hour and meters per second.

7. Train Crossing a Platform

$\mathrm{Time}=\frac{\mathrm{Length\; of\; Train}+\mathrm{Length\; of\; Platform}}{\mathrm{Speed}}$

The time taken for a train to cross a platform is the sum of the train’s length and platform length, divided by the speed.

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