Abicyclist pedals along a straight road with velocity, v, given in the figure below. she starts 7 miles from a lake; positive velocities take her away from the lake and negative velocities take her toward the lake.

when is the cyclist farthest from the lake?

approximately how far away is she at this time? give a best estimate. (round your answer to the nearest whole number.)

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

(1 point) match the differential equations and their vector valued function solutions. you may wish to multiply at least one solution out fully, to make sure that you know how to do it. you can get the other answers quickly by process of elimination and just multiply out one row element.

Which are true about beta reactions? there will be more than one answer. a. it has no change b. it doesn't change the mass of the number c. it has a mass of 0.0005 atoms d. it causes transmutation.