The spring of a spring gun has force constant k = 400 n/m and negligible mass. the spring is compressed 6.00 cm and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring. the spring is then released, and the ball is propelled out the barrel of the gun. the barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. the gun is held so the barrel is horizontal. calculate the speed with which the ball leaves the barrel if you can ignore friction.

v = 6.93 m/s

Explanation:

given,

spring constant = k = 400 N/m

compression of spring = 6 cm = 0.06 m

mass of ball = 0.03 Kg

length of barrel = 6 cm

using energy conservation

KE of ball = PE of spring

v = 6.93 m/s

hence, the speed at which ball leaves the barrel will be equal to v = 6.93 m/s

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.