The average value of the squared speed does not equal the square of the average speed. To verify this fact, consider three particles with the following speeds; v1 = 1.20 m/s, V2 = 4.32 m/s, and v3 = 8.09 m/s. Calculate (a) the average value of the squared speed and (b) the square of the average speed. (a) Number Units (b) Number Units

The radius of a sphere is known to be  r = 6.27 ± 0.06 cm.  The volume of a sphere is given by  (4/3)?r3.  Find the absolute uncertainty and the percent uncertainty in the volume of the sphere. absolute uncertainty       cm3 percent uncertainty

the average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom.  What is the approximate density, in kilograms per cubic meter, of a nucleus?

The rate of change of altitude in cm/s of a bird is given by a′(t)=650ln(t+3). What is the total change in altitude between t=3 and t=7? Round your answer to the nearest whole number and do not include units.

The sides of a small rectangular box are measured to be 1.7 ± 0.015 cm, 2.05 ± 0.035cm, and 2.7 ± 0.11 cm long. In this problem you can approximate the percent error on a product or quotient of quantities by the sum of the percent error on each quantity.Calculate its uncertainty in cm3.

Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance and time according to this function v(t,x) = x/t. Your measured distance and time have the following values and uncertainties x 3 meters, x =0,1 meters and t 1.8 seconds and 5t = 1.5 seconds. What is the uncertainty in the average speed, bV ? Units are not needed in your answer.

How many significant figures are in the following numbers? (a) 100.0 ± 0.4(b) 4.000 ✕ 106(c) 4.20 ✕ 10-11(d) 0.0060

A partly-full paint can has 0.515 U.S. gallons of paint left in it. (a) What is the volume of the paint, in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area = 12.1 m²), how thick is the layer of wet paint? Give your answer in meters. (a) Number i 1.949 (b) Number i 312.1 Units m^3 v Units m^2

The sides of a small rectangular box are measured to be 1.7 ± 0.015 cm, 2.05 ± 0.035cm, and 2.7 ± 0.11 cm long. In this problem you can approximate the percent error on a product or quotient of quantities by the sum of the percent error on each quantity.Calculate its volume in cm3.

The density of platinum is 21.45 x 103 kg/m3. a. Calculate the volume (in m3/atom) occupied per platinum atom b. Estimate the atomic diameter (in m);(The estimate uses the approximation that it is a cubic volume) c. Using this estimation, calculate the thickness of a metal foil (in m) containing 2.0 x 101 atomic layers of platinum.