At tequals0, a train approaching a station begins decelerating from a speed of 140 mi/hr according to the acceleration function a(t)equalsnegative 1120 left parenthesis 1 plus 4 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 tequals0.3?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Air initially at 0.75 bar, 1000 k, and occupying a volume of 0.12 m^3 undergoes two processes. process 1-2: the air is compressed isothermally until the volume is halved. process 2-3: the air undergoes a constant pressure process until the volume is halved again. assume ideal gas behavior. a) determine the mass of the air, in kg. b) the work and the heat transfer for each of the two processes, in kj. (100 kj = 1 bar . m^3)

Abaseball is thrown from the outfield toward the catcher. when the ball reaches its highest point, which statement is true? (a)its velocity is not zero, but its acceleration is zero. (b) its velocity and its acceleration are both zero. (c) its velocity is perpendicular to its acceleration. (d) its acceleration depends on the angle at which the ball was thrown. (e) none of the above statements are true.