Convert the following units to stated units.
(i) 90 km/h to m/s
(ii) 10 MPa to GPa
The correct answer and explanation is:
(i) Convert 90 km/h to m/s:
To convert kilometers per hour (km/h) to meters per second (m/s), follow these steps:
- Start by noting the conversion factors:
- 1 km = 1,000 meters
- 1 hour = 3,600 seconds
- Now, divide the kilometers by 1,000 to convert to meters, and divide the hours by 3,600 to convert to seconds.
- So, 90 km/h can be written as: 90 km/h=90×1000 m1 km×1 h3600 s90 \, \text{km/h} = 90 \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}}
- Simplifying the calculation: 90×10003600=90×518=25 m/s90 \times \frac{1000}{3600} = 90 \times \frac{5}{18} = 25 \, \text{m/s}
So, 90 km/h = 25 m/s.
(ii) Convert 10 MPa to GPa:
- MPa (megapascal) and GPa (gigapascal) are both units of pressure. The conversion between them is based on the fact that:
- 1 GPa = 1,000 MPa.
- To convert from MPa to GPa, divide by 1,000: 10 MPa=101000 GPa=0.01 GPa10 \, \text{MPa} = \frac{10}{1000} \, \text{GPa} = 0.01 \, \text{GPa}
So, 10 MPa = 0.01 GPa.
These conversions are fundamental in many areas of physics and engineering, where different unit systems are used based on scale. The km/h to m/s conversion is frequently used in speed or velocity calculations, especially in motion problems, while the MPa to GPa conversion is common in materials science and structural engineering to describe stress or pressure. Understanding unit conversions ensures accuracy when working across different measurement systems.