Problem 3: An Nd:YAG laser operates in a pulsed mode, with an energy of 100mJ (millimoles) per pulse, and a pulse repetition rate of 10Hz. Light can be emitted at 1065 nm, 532 nm, or 355 nm. (a) Each pulse lasts for 1ns, and in between pulses, no light is emitted. What is the instantaneous laser power during each pulse

Given Information:

Energy of laser pulses = E = 100 mJ = 100×10⁻³ Joules

Time = t = 1 ns = 1×10⁻⁹ seconds

Required Information:

Instantaneous power = P = ?

Explanation:

The instantaneous power is the power dissipated at any instant of time whereas the average power is the power dissipated over a given time interval.  

The instantaneous laser power during each pulse is given by

Where E is the energy of the laser pulses and t is the time that each pulse lasts.

or

Therefore, the instantaneous power of each pulse is 100 Mwatt.

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.