3:02AM Sat Mar 9 eoe ;e 2ag HCHW Ch 2 (31).pdf @) IS SR8 B AN 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 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 units of distance over time like meters per second. 2.2. a. A dogis running. If its velocity vector component is v = 0.4% then which picture of the dog is correct if using the standard orientation of the axis (seen below) where postive is to the right. T 1T T T T 71 -3 -2 -1 0 1 2 3 #1 H#2 b. Ifits velocity vector componentis 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 o -1 -2 -3 c. If a physics student says a cat's speed is |[v| = 0.4 % Explainin a short sentence why you don't know if the cat is moving left or right. d. A dog moves with initial position x; = 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 0 1 2 3 4 5 6 7 Q Notifications 3:02AM Sat Mar 9 Goo = 80% W) & 2ag HCHW Ch 2 (31).pdf Oy N e. Suppose a dog moved so that its initial postion was x = +1m and the magnitude of its displacement vector was |[Ax| = 5m. Explainin 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 word in the second: It's speed is m/s and its direction is . Assume the standard orientation of the axis where postive is the right. 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? S \"-\\ 3 - 3 = W 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. B > _ feet -10 o 10 20 30 40 S50 The jogger moves from point A to point B. Assume distance units of feet [ft] a. Onan 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 Q Notifications 3:02AM Sat Mar 9 (XY} & 2ag HCHW Ch 2 (31).pdf @] G I3 PN 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) (i) position (ii) displacement (iii) time (iv) distance (v) velocity (vi) speed (vii) acceleration 7.C. 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? - + 8 B8 -7 -6 - 5 6 7 8 9 10 - 5 4 3 2 14 0 1 2 3 4 10 d. Ifavector 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 letters. 8.6. a. Draw the addition of the two force vectors on a separate sheet: this is called the net force or total force fnet = f')l + f')z. HELP: Use the tail-to-tip drawing rule - = F, F _ b. Suppose l has size 6 and z 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 net = 171 + }72 on a separate sheet d. Suppose p; has size 8 and p, has size 4. What is the size (positive) of Ppe;? 9.6. a. Two position vectors are seen. Draw the displacement , , on a separate sheet. HELP: Use the tip-to-tip drawing rule X A Xy b. Suppose ; has magnitude 6 and X, has magnitude 2. What is the magnitude of AX = X, , 19 Calendar Q Notifications 3:02AM Sat Mar 9 LX) ISR G B & 2ag HCHW Ch 2 (31).pdf Oy N c. Two velocity vectors are seen. Draw the difference , , . Suppose #; has magnitude 5 and , has magnitude 10. What is the magnitude of AU ? 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. Asecond 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 o 10 20 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. x,=3m, x, =7m #2. x1 =7m, x5, =3m 12.C. (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 k) Calendar U To Do Q Notifications @ 11194 3:02AM Sat Mar 9 LX) ISR G B & 2ag HCHW Ch 2 (31).pdf Oy N (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, 2s, 3.86s, or 11.774s. b. Compute the car's average velocity from Os to 3s Ax HELP: Uavg = E 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 v: how is it different than average velocity v,,,, 1. Average velocity V4 is always computed between two times ty, 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(t1) = Vgpg When t; is close to t; approximately equal to In a physics experiment a toy car moves with position function x(t) = 0.15 a l_'_l function notation Fill out the two tables below (the first row is done for you already) m | mtonuos | assms 18 75 ' Vgapg from 1sto 2s Vgang from 1sto 1.5s Vang from 1sto 1.1s Vapg from 1s to 1.01s What is the best approximation to the car's instantaneous velocity at 1s? ANS: 0.45 Q Notifications 3:02AM Sat Mar 9 eoe ;e 2ag HCHW Ch 2 (31).pdf @] Gl O Z8 B AN 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 instantaneous velocity values are always (a word that starts with the letter \"e\"). Type 2. x-t graph is a parabola. See lecture notes page 12. c. Complete the sentence. If the x-t graph is a parabola, then the v-t graph has the shape of a tilted (two words), and the constant acceleration has a value that is the (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 acceleration values are always (a word that starts with the letter \"e\"). 16.C. Our physics 2ag class concentrates on \"simple motion\3:03 AM Sat Mar 9 . . . 80% +2aAx @ v=v,+at , Av=at (4) x=x0+(v;v)t , Mz(%)m Give a sentence description of each of the variables: x,xy, Ax = x x4, v,vq,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/sz . The plane has a final take off velocity of v = 130/. S g:] S . 0 710m a. The 4 kinetic equations below have the following 6 variables: xo, vy, x, v, a, t @) v=v,+at , Av=at (4) x=x0+(v\"2+vjt , M:(VO+V)N 10 Q Notifications 3:03AM Sat Mar 9 (XY} & SR E B 2ag HCHW Ch 2 (31).pdf @] 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. Whatis 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. \\_4 oKX N, + 0 710m 25.C. a. What is \"free fall motion\". Describe it in a short sentence. 3 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. d 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 acceleration and simply replace a with g, that is to say a = 9.8 Sz 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 componenta = g = 9.8 Sz ora=g= 9.8?2 ? 26.C. a). The \"magnitude\" of a vector is its size. Every magnitude is always positive: yes, or no? B : 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? e If a vector is a positive number, then which way does it point (north or L ; south)? I v @ Lo 11 Q Notifications PN 3:03AM Sat Mar 9 (XY} & 2ag HCHW Ch 2 (31).pdf Q SR E B PN c). A student is doing a free fall problem on a baseball thrown vertically upward. He finds that at a particular instantthat x = +5m, v = +3m/s and a = 9.8m/s?. If you think of the origin as the earth's surface, then draw and lable the three vectors: position , velocity , and acceleration d 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. 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). Astudent 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. Aballis thrown into the air with an initial speed vy =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? o0 c. What is the acceleration and velocity at 1.6s? d. What is the acceleration and velocity at 2.3s? e e. What is the ball's velocity and speed when it hits the 19m/s ground? I HELP: speed is a scalar and represents the magnitude of the velocity vector, so it is always positive. Speed can be found, s y e like all magnitudes for one-dim vectors, by taking the absolute value of the vector. 28.22. 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. AT d. Inchapter 16 we will study the Heat Conduction Equation % =-A v 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? 12 Q Notifications 3:03AM Sat Mar 9 (XY} & 2ag HCHW Ch 2 (31).pdf @] SR E B PN 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 variable t but instead has a value for all times. HELP: the word starts with \"c\" With the simple type of motion we study in 2ag, give a description for each of the two cases seen below. Inthe blanks below that say (SHAPE) use only from the 4 choises listed below: \"parabola\