To practice problem-solving strategy 25.1 power and energy in circuits. a device for heating a cup of water in a car connects to the car's battery, which has an emf e = 10.0 v and an internal resistance rint = 0.08 ω . the heating element that is immersed in the cup of water is a resistive coil with resistance r. david wants to experiment with the device, so he connects an ammeter into the circuit and measures 10.5 a when the device is connected to the car's battery. from this, he calculates the time to boil a cup of water using the device. if the energy required is 100 kj , how long does it take to boil a cup of water?

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.