A particle initially located at the origin has an acceleration oft? = 2.003 m/s2 and an initial velocity of ?i = 9.00i m/s. )Find the vector position of the particle at any2 time t m(where I: Is measured in seconds). laClv r-+_v (b) Find the velocity of the particle at any time t. (CH? i+_v film/5 (c) Find the coordinates of the particle at t = 1.00 s. x=v m y=v .. (d) Find the speed of the particle at t = 1.00 s. 9.0m + 2.00j x Remember that the constant acceleration equations are used separately for the X direction and for the y direction. m NASA's Ames Research Center in Mountain View, California, houses a 20g centrifuge used to conduct research and training to solve real world problems related to the effects of acceleration on systems. It consists of a horizontal rail system with a 58-foot diameter mounted on a central axis, as shown in the figure below. An astronaut is using the centrifuge for training on high accelerations during spaceflight. The astronaut is seated 29.0 ft from the axis of rotation. At what rotation rate, in revolutions per second, will the astronaut experience a centripetal acceleration of 18.9g? 29 ft 6.0 X How is centripetal acceleration related to speed? How is speed, in circular motion, related to angular speed? Can you use the angular speed to find the number of revolutions per second? rev/sIt is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope can view such objects using an electron beam instead of a light beam. Electron microscopy has proved invaluable for investigations of viruses, cell membranes and subcellular structures, bacterial surfaces, visual receptors, chloroplasts, and the contractile properties of muscles. The "lenses" of an electron microscope consist of electric and magnetic fields that control the electron beam. As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x axis in the xy plane with initial velocity v, = vi. As it passes through the region x = 0 to x = d, the electron experiences acceleration a = axi + a j, where a, and a, are constants. For the case v; = 1.96 x 10' m/s, ay = 8.89 x 1014 m/s2, and ay = 1.56 x 1015 m/s2, determine the following at x = d = 0.0100 m. (a) the position of the electron YF = m (b) the velocity of the electron VF = 2.00 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s i + 7.87 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s j (c) the speed of the electron IVl = 2.15 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s (d) the direction of travel of the electron (i.e. the angle between its velocity and the x axis) 0 = 21.5 X Your response differs from the correct answer by more than 100%