An observer is stationary in the inertial system s. a car is moving in the xdirection with speed v = √c 2 with respect to the observer in s. the driver of the car is stationary with respect to the car, and thus the driver is in a different inertial frame s 0 . the passenger of the car takes out a baseball, opens the sunroof of the car and throws out the ball with a velocity vb = √c 2 . (a) if the baseball is thrown in the x-direction (in the same direction the car is moving), what is the speed of the baseball as seen by the observer in s? (b) if the baseball is thrown in the minus x-direction (opposite to the direction the car is moving), what is the speed of the baseball as seen by the observer in s? (c) if the baseball is thrown in the y-direction (perpendicular to the direction the car is moving), what is the velocity (in direction x, y and z) of the baseball as seen by the observer in s (give all three velocity components! )

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.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2