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Unit 1: Mathematics for engineering LO1: Understand the application of algebra relevant to engineering problems Linear simultaneous equations Activity 1 Kirchhoff’s Laws can be used to analyse the voltages and currents flowing through parts of a circuit like the one shown in the picture. I1 10V I2 (I1 + I2) Part of the circuit is illustrated here – which 20V includes two voltage sources and three resistors. When Kirchhoff’s Laws are applied the currents are as follows: 7 8 2 10 V = 7I1 + 8 (I1 + I2) 20 V = 2I2 + 8(I1 + I2) Solve the equations by re-writing them as linear simultaneous equations, to find the values of currents I1 and I2 Version 1 Activity 2 Look at the roller coaster in the picture. On a straight downhill descent with constant acceleration, a ms-2, the distance travelled is given by the equation: s = ut + ½ at2 Where s is distance travelled, u is initial velocity, t is time and a is acceleration. If: distance s = 24m at t = 2s, and distance s = 88m at t = 4s Determine, using linear simultaneous equations: (a) Initial acceleration (in ms-2) (b) Initial velocity (in ms-1) (c) Distance travelled after 5 seconds Version 1