Mechanics 2 2.1 Motion
Learning objectives
This section is an introduction to the basic concepts used in describing motion. We will begin with motion in a straight line with constant velocity and then constant acceleration. Knowledge of uniformly accelerated motion allows analysis of more complicated motions, such as the motion of projectiles.
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Kinematical quantities
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We will begin our discussion of motion with straight line motion in one dimension. This means that the particle that moves is constrained to move along a straight line. The position of the particle is then described by its coordinate on the straight line (Figure 2.1a). If the line is horizontal, we may use the symbol x to represent the coordinate and hence the position. If the line is vertical, the symbol y is more convenient. In general, for an arbitrary line we may use a generic name, s, for position. So in Figure 2.1, x = 6 m, y = −4 m and s = 0.
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–3 –2
–4
s /m
–1 0 1 2
b
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s
4
–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x /m a
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3
y/m –4 –3 –2 –1 0 1 2 3 4
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Understand the difference between distance and displacement. Understand the difference between speed and velocity. Understand the concept of acceleration. Analyse graphs describing motion. Solve motion problems using the equations for constant acceleration. Discuss the motion of a projectile. Show a qualitative understanding of the effects of a fluid resistance force on motion. Understand the concept of terminal speed.
∆s
c
Figure 2.1 The position of a particle is determined by the coordinate on the number line.
∆s
∆t
∆t
As the particle moves on the straight line its position changes. In uniform motion the graph of position against time is a straight line (Figure 2.2). In equal intervals of time, the position changes by the same amount. This means that the slope of the position–time graph is constant. This slope is defined to be the average velocity of the particle: v=
0
t
Figure 2.2 In uniform motion the graph of position versus time is a straight line.
s t
where s is the change in position. The average velocity during an interval of time t is the ratio of the change in position s during that time interval to t.
2 MECHANICS
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