Scenario: The British manufacturing company that you work for has just installed two new machines. An American made CNC lathe and a German Press Brake. You are tasked with helping the commissioning team with some of the calculations needed to get these machines into production Task 1, The Press Brake 107 tunooord or Images sourced from Pixabay.com a. The tool on the press brake moves from the fully open (work loading) position to fully closed, x mm vertically in t seconds such that: x = 57t-9.2t Find: i. the initial velocity of the tool (mm s) ii. the time when the displacement of the tool is at a maximum the maximum displacement of the tool (mm) iii. iv. the actual velocity of the tool 0.25 s before it is fully open (work loading) position (mm s) b. Experimentation has shown that the hydraulic pressure in the press brake's cylinders can be modelled by the equation: P = 90+25.5 Ln 3t Determine: i. An expression for the rate of change of pressure with respect to time ii. The rate of change of pressure when t=1.5s iii. The time when the rate of change is 8 bar s- Where The back EMF (Volts) generated in the pump motors of the hydraulic press brake during the press cycle can be modelled as: E = 0.2t Sin 2nft os 2t E = EMF (V) f = Frequency of the supply voltage t = time in seconds c. Given that f is fixed at 50Hz, use differentiation to determine an expression for the rate of change of EMF during the press cycle. d. Use your expression to determine the rate of change of EMF (volts seconds ) at the time: t = 3.025 s