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{"ops":[{"insert":"Porcelain bottles are used to hold the well-known Japanese drink, sake. The bottles are filled up to the narrow neck. A certain line of these bottles is designed as shown right, with the internal radii in cm shown at levels, which differ in height by 4 cm\nThe internal volume of the bottle is given by \ud835\udc7d = \u222b A \ud835\udc85s, where ds is the vertical distance up the bottle, and \ud835\udc68 is the cross-sectional area. Estimate the internal volume correct to 3SF, using Simpson\u2019s Rule."},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Initial tests on a new type of electric car show that its maximum acceleration is given by the equation, \ud835\udc82= \ud835\udfd1t, where \ud835\udc82 is in \ud835\udc26s"},{"attributes":{"script":"super"},"insert":"\u2212\ud835\udfd0"},{"insert":" and \ud835\udc95 are in seconds."},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"i. Determine the velocity after 4 s of travel from rest at maximum acceleration\nii. What maximum speed, in km\/h, could the manufacturer claim that the vehicle can reach in 4 s?\niii. Find the distance travelled by the vehicle in this 4 s of travel time.\n"}]}
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