Question

1. determine the units of the quantity described by each of the following combinations of units:

a. kg(m/s)(1/s) b. (kg/s)(m/s²)
c. (kg/s)(m/s)² d. (kg/s)(m/s)

Explanation:

Step1: Recall unit - multiplication rules

When multiplying units, multiply the numerical parts and the unit parts separately. For example, if we have \(a\) with unit \(U_1\) and \(b\) with unit \(U_2\), then \(a\times b\) has unit \(U_1\times U_2\).

Step2: Solve part a

We have \(kg(m/s)(1/s)=kg\times m\times\frac{1}{s}\times\frac{1}{s}=kg\cdot m/s^{2}\). The unit \(kg\cdot m/s^{2}\) is the unit of force (Newton, \(N\)).

Step3: Solve part b

\((kg/s)(m/s^{2})=\frac{kg}{s}\times\frac{m}{s^{2}}=\frac{kg\cdot m}{s^{3}}\).

Step4: Solve part c

\((kg/s)(m/s)^{2}=\frac{kg}{s}\times\frac{m^{2}}{s^{2}}=\frac{kg\cdot m^{2}}{s^{3}}\).

Step5: Solve part d

\((kg/s)(m/s)=\frac{kg\cdot m}{s^{2}}\), which is the unit of force (Newton, \(N\)).

Answer:

a. \(kg\cdot m/s^{2}\)
b. \(kg\cdot m/s^{3}\)
c. \(kg\cdot m^{2}/s^{3}\)
d. \(kg\cdot m/s^{2}\)