Determine the units of the quantity described by the following cobinations of units.
a) kg (m/s) (1/s)
b) (kg/s) (m/s^2)
c) (kg/s) (m/s)^2
d) (kg/s) (m/s)
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To determine the units of the given quantities, we need to multiply and divide the given units according to the operations indicated.
a) kg (m/s) (1/s):
- The units within the parentheses are being multiplied: (m/s) * (1/s) = m/s^2
- Therefore, the units of the quantity described by this combination are kg * m/s^2.
b) (kg/s) (m/s^2):
- The units within the parentheses are being multiplied: (kg/s) * (m/s^2) = kg * m / (s^2 * s)
- Simplifying the units, we have: kg * m / s^3
c) (kg/s) (m/s)^2:
- The units within the parentheses are being squared and then multiplied: (kg/s) * (m/s)^2 = kg * m^2 / s^3
d) (kg/s) (m/s):
- The units within the parentheses are being multiplied: (kg/s) * (m/s) = kg * m / (s * s)
- Simplifying the units, we have: kg * m / s^2
To summarize:
a) The units are kg * m/s^2.
b) The units are kg * m / s^3.
c) The units are kg * m^2 / s^3.
d) The units are kg * m / s^2.