An alpha particle which is the same as a helium-4 nucleus, is momentarily at rest in a region of space occupied by an electric field. the particle then begins to move. find the speed of the alpha particle after it has moved through a potential difference of ? 3.45×10? 3 v .the charge and the mass of an alpha particle are q? = 3.20×10? 19 c and m? = 6.68×10? 27 kg , respectively. if you had carried out the algebra using variables before plugging numbers into your expressions, you would have found that(vf)? =? 2q? ? ? v is measured in volts. to verify that this expression for (vf)? has the correct units of velocity, you need to perform some unit analysis. begin by finding the equivalent of a volt in terms of basic si units. what is a volt in terms of meters (m), seconds (s), kilograms (kg), and coulombs (c)?

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?