Mechanics 1.10. Displacementtime and Velocity （1.10力学。）.pdfVIP

Mechanics 1.10. Displacement-time and Velocity-time graphs In leaflet 1.9 several constant acceleration formulae were introduced. However, graphs can often be used to describe mathematical models. In this case two types of graph are commonly used. 1. Displacement-time graphs. Any point on such a graph has coordinates (t,s), in which s is the displacement after a time t. Worked Example 1. Figure 1 shows the displacement-time graph for a tennis ball which is thrown vertically up in the air from a player’s hand and then falls to the ground. The graph illustrates the motion of the ball. s (m) Taking the origin to be the starting point, the 3.0 ball moves upwards (in the positive direction) to a maximum height of 2.5 m above the origin. It 2.0 stops momentarily and then drops to the ground, 1.0 which is 1.5 m below the initial release. t (s) Consequently, the velocity of the ball changes 0.5 1.0 2.0 from positive (on the way up) to 0 at the top -1.0 and then to negative (on the way down). -2.0 Figure 1 The gradient of a displacement-time graph is velocity 2. Velocity-time graphs. Any point on such a graph will have coordinates (t,v), in which v is the velocity after a time t. Worked Example 2. Figure 2 shows the velocity-time graph for the motion of the tennis ball described in example 1. It was thrown into the air with a velocity of v (ms -1) 7 m s−1. It has zero velocity at 0.71 seconds and