At tequals0, a train approaching a station begins decelerating from a speed of 96 mi/hr according to the acceleration function a(t)equalsnegative 1536 left parenthesis 1 plus 8 t right parenthesis superscript negative 3 mi/hrsquared, where tgreater than or equals0. how far does the train travel between tequals0 and tequals0.1? between tequals0.1 and tequals0.4?

Match each vocabulary term to its definition. 1. electrons neutral subatomic particles found in the nucleus of the atom 2. neutron lowest energy position of an electron in an atom 3. photon the path of an electron around the nucleus of an atom 4. ground state negatively charged, subatomic particles 5. protons packet of energy of specific size 6. element substance with only one type of atom 7. orbital positively charged, subatomic particles found in the nucleus of the atom

You throw a small rock straight up from the edge of a highway bridge that crosses a river. the rock passes you on its way down, 7.00 s after it was thrown. what is the speed of the rock just before it reaches the water 28.0 m below the point where the rock left your hand? ignore air resistance.

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s