# OCR Level 3 Cambridge Technicals in Engineering, Lesson ```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 + &frac12; 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
```