21.16. t [s] a. Whatis 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. Q Notifications 3:03AM Sat Mar 9 L Oy ) &I 2ag HCHW Ch 2 (31).pdf Q M 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. Isthe 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 2t?, 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 | | I I | |"||''|'||% meter -0 9 8 -7 6 -5 4 -3 -2 - o 1 2 3 4 5 8 7 8 9 10 HELP: recall that the position vector is drawn with its tail at the origin but , d 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 1 M) x=x +tyt+oat, Av=vt+oat | @) Vi=vl+2a(x-xy), v' =v,> +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 Ll ol SN B I pEr s (o Ao A HN NN Q M 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. . 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. O o \\{n{{ . o 710m