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# Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf X W2ag HW Ch 1 (20) - Physics 2ag X /Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31)

## Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf X W2ag HW Ch 1 (20) - Physics 2ag X /Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31) %20(1).pdf f o search Hi 2/14 - I + 90% + 1.1 a. Put in two words: A train moves with one-dimesional motion. This means along the x-axis below the train can either move or -7 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 b. Draw the postion and velocity vector for each train above. c. How you draw the size of the velocity vector of each train is unrelated to the size of each position vector. Explain why. Give a short sentence as your answer. ANS: the position vectors have units of distance like meters but the velocity vectors have 2.2. units of distance over time like meters per second. 77L then which picture of the a. A dog is running. If its velocity vector component is v = -0.4- dog is correct if using the standard orientation of the axis (seen below) where postive is to the right. -3 -2 -1 1 2 3 #1 #2 5 b. If its velocity vector component is v = 0.4 then which picture is correct if using the non- standard axis seen below where postive is now to the left. 3 2 1 0 -1 -2 -3 #1 #2 S c. If a physics student says a cat's speed is lvl = 0.4. Explain in a short sentence why you don't know if the cat is moving left or right. d. A dog moves with initial position x1 -2m with net displacement Ax=-5m. Draw the initial and final position vectors (arrows) of the dog below. HELP: recall that postion vectors are drawn with their tail at the origin and tip at the location of the object. The dog must have final postion x = 7m -7 -6 -5 -4 -3 -2 -1 o 1 2 3 4 5 6 7 SAMSUNG 2 Activate Windows Go to Settings to activate Window ED 12: 3/9 x Topic: I made a couple changes X 2ag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics 2ag + Desktop%20user/Downloads/2ag%20HCHW%20Ch%202% 20 (31)%20(1).pdf to search 3/14 - 90% + e. Suppose a dog moved so that its initial postion was x = +1m and the magnitude of its displacement vector was |Ax] = 5m. Explain in a short setence why you don't know if the dog's final position is - 4m or + 6m. 3.3. - a. The dog seen below moves with velocity v = -1.5. Put a number in the first blank and a Assume the word in the second: It's speed is m/s and its direction is standard orientation of the axis where postive is the right. 771 S b. Suppose also that a cat moves with velocity v = -3.0. Draw the velocity vector on each animal below and comment on the drawing scale: i.e., how much longer is the cat's velocity vector compared to the dogs? 4.4. A quick way to see if a variable n represents a vector component or a scalar is to add the phrase "in the direction east" and see if that sentence makes sense. Do that to each below and state if the variable represents a scalar or vector a. A force of F = 10 lbs was applied to the brick b. Juan drank V = 2 Liters of Pepsi. 5.C. A Pi -10 0 10 20 30 40 50 feet The jogger moves from point A to point B. Assume distance units of feet [ft] a. On an axes with no numbers you will often see a + and/or - symbol at the end of the axis like + What purpose does the + sign serve? Explain in a short sentence. HELP: See problem 2.2a,b. b. In the diagram above, what is the jogger's initial position? c. What is the jogger's final position? d. What is his displacement? e. What distance did he move? f. Draw both position vectors and the displacement vector in the picture above. HELP: the displacement vector has its tail at the initial position and tip at the final position. 6.C. a. Some quantities in physics are not just numbers but are considered a geometric arrow (having both a size and direction). These quantities are called SAMSUNG 3 Activate Windows Go to Settings to activate Windows. 4 E 12:16 AM 3/9/2024 Topic: I made a couple changes X 2ag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics 2ac X + s/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202% 20 (31)%20(1).pdf df ere to search 4 / 14 90% + b. Physics quantities that are not arrows (i.e., don't have a direction) are called c. Classify each as a scalar (S) or vector (V) 7.C. (i) position (ii) displacement (iii) time (iv) distance (v) velocity (vi) speed (vii) acceleration a. When you add two vectors you get another vector: yes or no? b. When you subtract two vectors you get another vector: yes or no? c. Given the coordinate system below where increasing numbers are to the right and decreasing numbers are to the left, any vector component that has a negative value must point left or right? H ++ -10 9 -6 -5 4 -2 =1 D 7 4 7 B 5 B 9 10 d. If a vector has a positive component, then which way does it point for the axis above? e. The magnitude of a vector means its size. Size is always a positive number. The magnitude of any one-dimensional vector can be found by taking its absolute value: yes, or no? ANS: yes. f. What is the quick name given to "the magnitude of the velocity vector". HELP: it starts with the letter s. 8.6. a. Draw the addition of the two force vectors on a separate sheet: this is called the net force or total force Fret = F+F. HELP: Use the tail-to-tip drawing rule F F b. Suppose F has size 6 and F has size 2. What is the size of Fnet? HELP: recall that the size of a vector is called its magnitude and is always a positive quantity. c. Two momentum vectors are seen below. Draw Pnet = P1 + P2 on a separate sheet P1 P2 d. Suppose p has size 8 and p has size 4. What is the size (positive) of Pnet? 9.6. a. Two position vectors are seen. Draw the displacement 2- on a separate sheet. HELP: Use the tip-to-tip drawing rule x2 i b. Suppose, has magnitude 6 and 2 has magnitude 2. What is the magnitude of Ax=2-1 SAMSUNG A Activate Windows Go to Settings to activate Windows. - 12:16 AM 3/9/2024 X X Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics Zag X + ers/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31) %20 (1).pdf pdf here to search Et 5/14 - 90% + c. Two velocity vectors are seen. Draw the difference 2-1. Suppose v has magnitude 5 and v has magnitude 10. What is the magnitude of Av? v2 v1 10.8. a. A car moves one-dimensionally. It starts at x = 15m then moves a distance of 200m to the right, then 100m left. Find the total distance moved and displacement of the car for the entire motion. As part of your work draw the path of the car and the following vectors: initial position, final position and displacement. ANS: 300, 100 b. A second car starts at -20m and drives 50m to the right in 4s then moves 80m left in 6s. Find its initial and final position, net displacement, total distance moved, average speed and average velocity. Indicate which are scalars(S) and which are vectors(V). Draw the object at the initial and final positions (ok to draw the car as a box0 and draw all vectors involved on the axis below. -40 -30 -20 -10 10 20 -8 30 40 11.C. Displacement Ax is often interpreted as a "directed distance". Explain what the difference is between "distance" and "directed distance". As a feel for what this question is asking, consider the two situations below for the initial and final positions of a moving object. #1. X1 3m, x2 = 7m 12.C. #2. x =7m, x2 = 3m m (a). Car #1 has position x = -40m and velocity v = 3. Car #2 has position x = 10m with velocity v = -9 Draw the cars and the associated vectors below. meter -40 -30 -20 -10 O 10 20 30 40 SAMSUNG 5 a Activate Windows Go to Settings to activate Windows. A 12:16 AM 3/9/2024 Topic: I made a couple changes X 2ag HCHW Ch 2 (31) (1).pdf 2ag HW Ch 1 (20) - Physics 2a X + rs/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202% 20 (31)%20(1).pdf df e to search 6/14 - 90% + (b). How much longer should car #2's velocity be drawn compared to car #1? (c). Explain why you can't compare a position vector's size to a velocity vector's size. 13.C. Suppose remote-control toy car can move backward/forwards according to the equation X= 2t3 - 5t where position is in [m] and time in [s] a. True or false: the t variable in this equation is an "instant" of time and can be any real number like 0, 0.3s, 25, 3.86s, or 11.774s. b. Compute the car's average velocity from Os to 35 HELP: Vavg = Ax At 14.E. Average velocity is always computed between two instants in time (called a time interval) whereas instantaneous velocity is always computed at one instant in time. We explore how these two (average versus Instantaneous) are related below. Instantaneous velocity : how is it different than average velocity Vavg 1. Average velocity varg is always computed between two times t, t 2. Instantaneous velocity v is the velocity at one instant in time t and is approximately equal to the average velocity if the time interval At = t- t is small. v(t)vavg when t is close to t approximately equal to In a physics experiment a toy car moves with position function x(t) = 0.15t function notation Fill out the two tables below (the first row is done for you already) time [s] position [m] 5 18.75 2 1.5 1.1 1.01 Vava from 1s to 5s 4.65 m/s Vavg from 1s to 2s Vang from 1s to 1.5s Varg from 1s to 1.1s Varg from 1s to 1.015 Q 1 What is the best approximation to the car's instantaneous velocity at 1s? ANS: 0.45 Activate Windows Go to Settings to activate Windows. SAMSUNG 8 12:16 AM 3/9/2024 X Program Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics 2ag x + File C:/Users/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31)%20(1).pdf Ch 2 (31) (1).pdf Type here to search 7 / 14 1 90% + 15.C. General motion has curvy x-t graph that gives rise to curvy v-t and a-t graphs that require Calculus to analyze instantaneous values. To avoid Calculus in this class our x-t graphs will be of only TWO types. Type 1. x-t graph is straight and tilted. Describe what the v-t and a-t graphs look like Type 1. x-t grah is a tilted straight line. HELP: See lecture notes at bottom of page 11. a. Complete the sentence. If the x-t graph is a tilted straight line, then the constant velocity has a value that is the (a word that starts with the letter "s") of the x-t line and the acceleration has the value (a number) b. Complete the sentence: If the x-t graph is a tilted straight line then the average and (a word that starts with the letter "e"). instantaneous velocity values are always Type 2. x-t graph is a parabola. See lecture notes page 12. a tilted is the c. Complete the sentence. If the x-t graph is a parabola, then the v-t graph has the shape of (two words), and the constant acceleration has a value that (a word that starts with the letter "s") of the v-t line. d. Complete the sentence: If the x-t graph is a parabola then the average and instantaneous (a word that starts with the letter "e"). acceleration values are always 16.C. Our physics 2ag class concentrates on "simple motion", that is, motion in which the acceleration is constant (whether 0 or non zero). This is seen in problem 15.C above. Under constant acceleration, the three graphs of x-t, v-t, a-t will have PREDICTABLE fixed shapes with predictable slopes of all straight lines involved. Even though not emphasized for this class (but in more difficult classes), we exploare how to find the instantaneous velocity from average velocity when the x-t graph is curvy but NOT NECESSARILY A PARABOLA. (see below). x [m] Average velocity 1. Instantaneous velocity at I, from 1 to 2 provided 12 is close to 2. v(t)= provided Al is small 44 (2x2) worst approximation somewhere inbetwen the worst and the best 0 Dotted line is the instantaneous velocity att (12+x2) (4.1) 4, close to each other 2 far from each other SAMSUNG best spproximation [[3] Activate Windows Go to Settings to activate Windows. : ~8 12:17 AM 3/9/2024 +6 X -Topic: I made a couple changes X > Zag HCHW Ch 2 (31) (1).pdf X Zag HW Ch 1 (20) - Physics 2ag X | + ers/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31)%20(1).pdf .pdf here to search 8/14 - 90% + Suppose now that an object moves with x-t equation x = 3 cost graphed below. Assume t is in seconds and x is in meters. a. We want the instantaneous velocity at t = 2s using the average velocity formula. Explain (using a short sentence) why case 2 below would give the better approximation. Case 1. Use t = 3s Case 2. Use t = 2.1s HELP: See problem 16.C. Read the boxed info. b. Based on your answer in part (a), approximate the instantaneous velocity at 2s. HELP: Make sure your calculator is in RADIAN mode for your computation. ANS: 2.66 m/s 17.14. A child operates a remote-controlled toy car on a linear track. The figure below plots the car's position as a function of time (x-t graph). a. Explain how you know this motion has a constant acceleration of 0 for each straight line segment of motion seen in the graph. HELP. See the bottom of page 11 of lecture notes. Find the velocity (in m/s) of the toy car over the following time intervals. Indicate the direction with the sign of your answer. b. from 0s to 2 s x (m) 4 3 2 c. from 2 s to 4s d. from 4 s to 6 s e. from 6s to 9s f. from 2 s to 6s t(s) 9 10 18.C. A person who is learning to drive travels backwards and forwards in a straight line in an empty parking lot. Below is a graph of his motion. V [mile/hour] 3 Average t 0 5 [min] SAMSUNG 8 8 Activate Windows Go to Settings to activate Windows. A 12:17 AM 3/9/2024 ogram X Topic: I made a couple changes X 2ag HCHW Ch 2 (31) (1).pdf WA2ag HW Ch 1 (20) - Physics 2a x + File C:/Users/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31) %20 (1).pdf 2 (31) (1).pdf Type here to search Hi 9/14 90% + a. How would you classify the graph above. Circle one the choices: (i) x-t, (ii) v-t, (iii) a-t. b. Looking at the graph, is the velocity changing every instant: yes, or no? HELP: does this velocity graph have a different height at each instant in time. c. True or False: the average velocity 3 mph is a good measure of the center of the car's fluctuating velocity (see dotted line in the graph). d. Was there a time(s) in which the car stopped (i.e. the car was momentariy at rest). If yes, then state the time(s). HELP: an object is momentarily at rest at instant t if its velocity is 0 at t. e. If we think of the positive parts of the graph (graph above t axis) as the car moving east, was there any time at which the car moved west: yes, or no? If yes, then state the time interval(s). For example, the form of your answer should look like "from 7 min to 10min". 19.9. a. Name three conditions that will cause a moving object to have a non-zero acceleration. HELP: See lecture notes at the top of page 8 in the box. b. A Ferrari car can go v =0 to v = 30 in At = 2.6s Calculate it's acceleration and state by how much the car increases is velocity for each second that goes by. 20.9. A large rubber ball has a speed of 4.0 m/s and moves to the right but once its hits the wall it travels at 2.0 m/s to the left. If it was in contact with the wall for 0.40s, then find the balls average acceleration. Draw pictures to help visualize the velocity vectors 21.16. v [m/s] -10 (9, 18) (13,8) (18, 0) t[s] (0.-12) (4.-12) a. What is the instantaneous velocity at 5s? From the sign, state if the object is moving toward increasing x (right) or decreasing x (left). b. What is the average acceleration from 4s to 9s? c. What is the instantaneous acceleration at 7s? HELP: Since the v-t graph from 4s to 9s is a straight line means the acceleration is constant. This means the instantaneous acceleration at any particular time from 4s to 9s is equal to the average value from 4s to 9s. Activate Windows Go to Settings to activate Windows. SAMSUNG A @4 12:17 AM 3/9/2024 Topic: I made a couple changes X 2ag HCHW Ch 2 (31) (1).pdf WA2ag HW Ch 1 (20) - Physics 2ag X + sers/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31)%20(1).pdf .pdf pe here to search 10/14 - 90% + d. Is the object speeding up or slowing down at 5s? Explain how you know. HELP: See boxed rule in lecture notes p.14. e. Is the object speeding up or slowing down at 7s? f. Between what two times is the object moving toward decreasing x (i.e. left). g. Yes/No: Is the velocity constant between 9s and 13s? What is its value? What does that mean for the value of the average and instantaneous acceleration values? 22.C. Suppose that a car moves one-dimensionally along the x-axis and has x-t equation x = 15-2t2, and v-t equation v = -4t, and a-t equation a = -4. Assume all variables are in the standard metric units [m], [m/s] and [m/s]. a. Compute the car's position, velocity and acceleration at 2s b. If the positive direction of the axis is to the right, then state if the car is moving toward increasing numbers on the axis (right) or decreasing numbers (left) at 2s. c. Draw the car below and draw three vectors: position, velocity, and acceleration at 2s meter -10 9-8 65 -7 4 3 2-1 0 1 2 3 4 5 B 7 8 9 10 HELP: recall that the position vector is drawn with its tail at the origin but v, a are drawn on the object pointing in the correct direction. d. Is the car speeding up or slowing down at 2s? Explain how you know. e. True or False: If velocity and acceleration are parallel vectors, the object is speeding up, and if they are anti-parallel then it is slowing down 23.C. For the special motion of constant acceleration, we have 4 kinematic equations that fully describe the motion seen below. (1) x = x+v+ at, Ax = vol+ ar | (3) v = vo+2a (x-x), v=vo+2aAx (2) y = v+at Av = at (4) x=x+ V+v 2 Ax= At 2 Give a sentence description of each of the variables: x, xo, Ax = x - xo, v, vo, a,t 24.19. A plane is at rest and located 710 m east of the control tower. A student uses the following reference frame (i.e. axis) with the tower at the origin and the positive x axis pointing to the right. Suppose the plane starts at rest and speeds up in the westerly direction with constant acceleration a = -1.5 m/s2. The plane has a final take off velocity of v = -130 m/s. 710m (1) x=x+v+al, Ax Ar = v+ a. The 4 kinetic equations below have the following 6 variables: xo, Vo, x, v, a, t (3)=v+2a (x-x), v=v2+2aAx V+V (2) v=v+at Av = at (4) x=x+ = 2 Ar- (vo) Af 10 10 SAMSUNG Activate Windows Go to Settings to activate Windows. 12:17 AM 3/9/2024 gram Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics 2ac x + - C:/Users/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202%20(31) %20 (1).pdf 2 (31) (1).pdf Type here to search 11/14 - 90% + Identify which of these 6 variables are known (i.e. given) at the start of this problem. b. Explain (using a short sentence) why both a, v are negative for this problem. c. Find the final position x of the plane when it takes off? As part of your work, explain why among the 4 kinematic equations you chose the one you did. d. What is the displacement Ax of the plane from start to take-off? Does it make sense that Ax is negative; explain. HELP: Which way is the vector pointing? e. What is the distance that plane moves d before taking off? f. Draw the following vectors on the picture below: initial and final positions, displacement, final velocity, and acceleration. 710m 25.C. a. What is "free fall motion". Describe it in a short sentence. b. Suppose that the positive axis is upward and negative axis is downward. Seen is a snapshot of a rock executing free fall motion. What is sign of its velocity and acceleration? Is the rock slowing down or speeding up? Explain how you know. c. When the rock reaches its maximum height what is the value of its velocity at that moment? d. When it reaches maximum height, its acceleration is still -9.8 m/s: yes, or no? e. True or False: to solve free fall motion problems, use the 4 kinematic equations for constant -9.8 acceleration and simply replace a with -g, that is to say a = = 77L f. Look at the notes: we see that the letter "g" is the magnitude of the acceleration vector. As a magnitude which is correct: g = 9.8 m/s or g = -9.8 m/s ? What is true about the sign of the magnitude of any vector? g. Using the standard direction of north/south axes where positive is up, when an object is in free fall is the vector component a = g = 9.8 or a=-g= -9.8 26.C. m 52 a). The "magnitude" of a vector is its size. Every magnitude is always positive: yes, or no? b). Given the coordinate system seen to the right, increasing numbers are upward and decreasing numbers are downward. Any vector with a negative value must point up or down? If a vector is a positive number, then which way does it point (north or south)? -6-5-4-3-2-1 0 1 2 3 4 5 6 SAMSUNG Q 8 11 Activate Windows Go to Settings to activate Windows. DE A 12:17 AM 3/9/2024 X ram Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf W2ag HW Ch 1 (20) - Physics 2ag X + C:/Users/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202% 20 (31)%20(1).pdf 2 (31) (1).pdf Type here to search Hi 12/14 - 90% + c). A student is doing a free fall problem on a baseball thrown vertically upward. He finds that at a particular instant that x = +5m, v = +3 m/s and a = -9.8 m/s. If you think of the origin as the earth's surface, then draw and lable the three vectors: position, velocity, and acceleration a on the axis seen to the right. HELP: Recall that position vectors have their tail at the origin and tip at the object and velocity and acceleration are drawn on the object. + -2 -1 0 1 2 3 4 5 6 d). For the numbers given in part (c), is the object slowing down or speeding up? Explain how you know with a short sentence. e). A student makes the statement "if at an instant, the accleration and velocity of an object have opposite signs then the object is slowing down". Is he correct? Yes, or no? f). A student makes the statement "if at an instant, the accleration and velocity vectors point in the same direction, then the object is slowing down". He is incorrect. Correct his statement. 27.21. A ball is thrown into the air with an initial speed vo =19 m/s from the height of a person's head, h = 1.6m. Choose the positive direction of the axis as upward like in the previous problem and the origin to be ground level. a. How high above the ground does the ball travel before turning around? b. How long is the ball in the air? c. What is the acceleration and velocity at 1.6s? d. What is the acceleration and velocity at 2.3s? e. What is the ball's velocity and speed when it hits the ground? HELP: speed is a scalar and represents the magnitude of the velocity vector, so it is always positive. Speed can be found, like all magnitudes for one-dim vectors, by taking the absolute value of the vector. 28.22. 19 m/s 1.6m 1 a. Our class meets from 7pm to 10pm. What is the duration At (i.e., elapsed time) b. Suppose that someone in the class had a stopwatch and as soon as class started, he used the stopwatch to keep track of class time. What number does any stopwatch start at when you hit start? What number would the stopwatch read at the end of class? c. You can see that parts (a) and (b) give the same answer of 3 hours True or false: when using any physics equation that involves time, if the student always sets the initial time to 0, then At gives the same number as t. d. In chapter 16 we will study the Heat Conduction Equation 9=- At AT Ax -A . In this equation T is temperature and t is time. Given your answer to part (c), how might you rewrite this equation for the time part? SAMSUNG 12 a Activate Windows Go to Settings to activate Windows. DE 12:17 AM 3/9/2024 Topic: I made a couple changes X Zag HCHW Ch 2 (31) (1).pdf 2ag HW Ch 1 (20) - Physics 2ag x | + /Users/Desktop%20user/Downloads/2ag%20HCHW%20Ch%202% 20 (31)%20(1).pdf (1).pdf Type here to search 13/14 - 90% 29.C. Prof. Scott has emphasized that in 2ag we are not required to know Calculus. Because of this, we study a very simple type of motion where the acceleration is not dependent on the time value for all times. HELP: the word starts with "c" variable t but instead has a With the simple type of motion we study in 2ag, give a description for each of the two cases seen below. In the blanks below that say (SHAPE) use only from the 4 choises listed below. "parabola", "straight line". HELP: See page 11 & 12 of the lecture notes Case 1: a = constant = 0 shape (i) Its x-t graph is a object's whose slope represents the constant value of the (HELP: starts with the letter "v") shape (ii) Its v-t graph is a constant The height to this horzontal line is the value of the (HELP: starts with the letter "v"). (iii) It's a-t graph is a value shape The height to this horizontal line at any time is the (HELP: put in a number). Case 2: a constant # 0 shape (i) Its x-t graph is a shape (!!) Its v-t graph is a object's whose slope represents the the constant value of the (HELP: starts with the letter "a"). shape (iii) It's a-t graph is value of the The height to this horizontal line at any time is the (HELP: starts with the letter "a"). 30.C. a. HCHW is a assignment that looks similar to examples done in lecture: true or false? b. If a problem is numbered 4.C. it means it's the 4th problem assigned and the problem explore concepts: true or false? c. Yes or no: the bottom of each cover page has the codes for how to interpret the numbering system. For instance 5.8 means it's the 5th problem assigned and it looks like example #8 in the lecture notes. 31.C. a. For each HCHW you must fill out the first couple of lines labled steps 1,2,3 and include that cover page as the first page of the assignment you turn into canvas: true or false? b. You are not allowed to write your solutions on these question sheets but instead you must write your them on separate sheets of paper (or tablet). The only exception to this rule is if there is a graph/drawing/table: true or false? SAMSUNG 13 Activate Windows Go to Settings to activate Windows. DE 14 12:18 AM 3/9/2024

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