Convert Units of Velocity: Step-by-Step Guide

Learn how to convert between different units of velocity (speed) with detailed solutions. Both metric and imperial units are covered. Conversions require both time and length unit conversions.

Time Conversion Reference

For length conversions, refer to the length conversion table.

Solved Velocity Conversion Problems

Question 1

Convert \(1 \text{ km/hr}\) into \(\text{inches/second}\).

Solution:

From the length conversion table: \(1 \text{ km} = 39370.07 \text{ inches}\).

Time conversion: \(1 \text{ hour} = 3600 \text{ seconds}\).

Therefore:

\[ 1 \text{ km/hr} = \frac{39370.07 \text{ inches}}{3600 \text{ sec}} = 10.9361 \text{ inches/sec} \]

Question 2

Convert \(12.34 \text{ miles/hour}\) into \(\text{centimeters/minute}\).

Solution:

Length conversion: \(1 \text{ mile} = 160934.4 \text{ cm}\).

Time conversion: \(1 \text{ hour} = 60 \text{ minutes}\).

Therefore:

\[ 12.34 \text{ miles/hour} = \frac{12.34 \times 160934.4 \text{ cm}}{60 \text{ min}} = 3.30988 \times 10^{4} \text{ cm/min} \]

Question 3

Convert \(60 \text{ miles/hour}\) into \(\text{meters/second}\).

Solution:

Length conversion: \(1 \text{ mile} = 1609.344 \text{ meters}\).

Time conversion: \(1 \text{ hour} = 3600 \text{ seconds}\).

Therefore:

\[ 60 \text{ miles/hour} = \frac{60 \times 1609.344 \text{ m}}{3600 \text{ sec}} = 26.8223 \text{ m/sec} \]

Question 4

The speed of light is approximately \(3 \times 10^{8} \text{ m/sec}\). Convert to \(\text{km/hour}\).

Solution:

Length conversion: \(1 \text{ m} = 0.001 \text{ km}\).

Time conversion: \(1 \text{ second} = \frac{1}{3600} \text{ hour}\).

Therefore:

\[ 3 \times 10^{8} \text{ m/sec} = 0.001 \times 3 \times 10^{8} \times 3600 \text{ km/hour} = 1.08 \times 10^{9} \text{ km/hour} \]

Question 5

Convert \(235 \text{ feet/second}\) into \(\text{meters/minute}\).

Solution:

Length conversion: \(1 \text{ foot} = 0.3048 \text{ m}\).

Time conversion: \(1 \text{ second} = \frac{1}{60} \text{ minutes}\).

Therefore:

\[ 235 \text{ feet/second} = \frac{235 \times 0.3048 \text{ m}}{(1/60) \text{ min}} = 4297.68 \text{ meters/minute} \]

For more practice, explore our math problems with detailed solutions.