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# CHAPTER 1

In this chapter, the applications of straight lines in engineering are introduced. It is assumed that the students are already familiar with this topic from their high school algebra course. This chapter will show, with examples, why this topic is so important for engineers. For example, the velocity of a vehicle while braking, the voltage-current relationship in a resistive circuit, and the relationship between force and displacement in a preloaded spring can all be represented by straight lines. In this chapter, the equations of these lines will be obtained using both the slope-intercept and the point-slope forms.

## 1.1 VEHICLE DURING BRAKING

The velocity of a vehicle during braking is measured at two distinct points in time, as indicated in Fig. 1.1.

Figure 1.1 A vehicle while braking.

The velocity satisfies the equation

where vo is the initial velocity in m/s and a is the acceleration in m/s2.

(a) Find the equation of the line v(t) and determine both the initial velocity vo and the acceleration a.

(b) Sketch the graph of the line v(t) and clearly label the initial velocity, the acceleration, and the total stopping time on the graph.

The equation of the velocity given by equation (1.1) is in the slope-intercept form y = mx + b, where ...

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