# Calculating density, acceleration, mass, and distance

Please give an answer and explanation with steps if needed.

1) A block of material has dimensions 3.8cm by 6.1 cm by 3.8cm. Its mass is 594g. What is the density? Answer in units of g/cm^3

2) An acceleration of 4.2 mi/h/s is equal to: Answer in units of m/s^2.

3) Grains of fine beach sand are assumed to be spheres of radius 57.7 micro meters. These grains are made of silicon dioxide which has a density of 2600 kg/m^3.

a) What is the mass of each grain of sand? in units of kg?

Then for the same problem consider a cube whose sides are 0.903 m long.

b) How many kg of sand would it take for the total surface area of all the grains of sand to equal the surface area of the cube? in units of kg.

4) Water flows into a swimming pool at the rate of 8.79 gal/min. If the pool dimensions are 20.7 ft wide, 44.4 ft long and 16.6 ft deep, how long does it take to fill the pool? ( 1 gallon = 231 cubic inches and answer in units of min.

5) A car travels along a straight stretch of road. It goes for 13.4 mi at 50 mi/h, then 29.5 mi at 43 mi/h, and finally 32.3 mi at 30.8 mi/h. What is the car's average velocity during the entire trip and answer in units of mi/h.

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#### Solution Preview

1.) Density = mass/volume = 594/(3.8*6.1*3.8) = 6.74 g/cm^3 --Answer

2.) Because 1 mile = 1609.3 m, and 1 hr = 3600 s

Therefore, acceleration

4.2 mi/h/s = 4.2*1609.3/3600 = 1.8775 m/s^2 --Answer

3.) a.) Radius of sand grain r = ...

#### Solution Summary

This solution provides brief calculations for each problem in order to calculate the necessary answers.