We would like to use the relation v(t)=i(t)r to find the voltage and current in the circuit as functions of time. to do so, we use the fact that current can be expressed in terms of the voltage. this will produce a differential equation relating the voltage v(t) to its derivative. rewrite the right-hand side of this relation, replacing i(t) with an expression involving the time derivative of the voltage. express your answer in terms of dv(t)/dt and quantities given in the problem introduction.

Identical marbles are released from the same height on each of the following four frictionless ramps . compare the speed of the marbles at the end of each ramp. explain your reasoning

You and a friend (alex) are at a a tree-top adventure park .. . part of the course requires you to climb up a rope. you both climb the same rope in the same amount of time. however, the tension in the rope is greater when alex climbs. who did the most work? alex did - more tension means more force - more force means more work was done you did - less tension means less force - less force means more work was done to find the work done, the force exerted and distance moved are multiplied. a couch is moved twice before you are happy with its placement. the same force was used to move the couch both times. if more work is done the first time it is moved, what do you know about the distance it was moved? when more work was done, the couch was moved less. when more work was done, the couch was moved further. when more work was done, the couch wasn't moved at all. when more work was done, the couch was moved the same distance.

How much energy is supplied to each coulomb of charge that flows through a 12-v battery?