Question

The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s². Use 1 ft = 30.48 cm to express this acceleration in units of m/s². (c) The density of water is 1.0 g/cm³. Convert this density to units of kg/m³.

Short answer

(a) The velocity in ft/s is 88 ft/s.

(b) The acceleration in m/s² is 18.3 m/s².

(c) The density in kg/m³ is 1000 kg/m³.

Step-by-step solution

Conversion in ft/s

Part (a)

The conversion in ft/s is shown below,

$$\begin{gathered} 60mph=60\frac{mi}{h}\times \frac{5280ft}{1mile}\times \frac{1h}{3600s} \\ 60mph=88ft/s \end{gathered}$$

Thus, the value in ft/s is 88 ft/s.

Conversion in m/s2

Part (b)

The conversion in m/s² is shown below,

$$\begin{gathered} 32ft/s^2=60\frac{ft}{h}\times \frac{30.48cm}{1ft}\times \frac{1m}{100cm} \\ 32ft/s^2=18.3m/s^2 \end{gathered}$$

Thus, the value in m/s² is 18.3 m/s²

Conversion in m/s2

Part (c)

The conversion in kg/m³ is shown below,

$$\begin{gathered} 1g/c{m}^3=1\frac{g}{c{m}^3}\times {\left(\frac{100cm}{1m}\right)}^3\times \frac{1kg}{1000g} \\ 1g/c{m}^3=1000kg/m^3 \end{gathered}$$

Thus, the value of density in kg/m³ is 1000 kg/m³.