Abook is given a sudden push to make it slide along a desktop. if the initial speed of the slide is doubled, by what factor is the distance that the book slides changed?

a 20 kg cart is moving at 2.0 m/s when a 5.0 n force is applied for a distance of 6.0 m in the direction the car is moving. what is the kinetic energy of the cart at the end of the 6.0 m?

a 0.145 kg baseball is thrown from a platform above the ground at a 10 m/s. the ball is moving 15 m/s when it strikes the ground. from what height above the ground was the ball thrown?

as a general rule, scissors have blades less than 6 in (15 cm) long and usually have handles with finger holes of the same size. shears have blades scissors used to cut hair or fabric must be much sharper.

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.