Kinematic equations can be applied to any motion for which the acceleration is constant. The verbal description of the motion was: An object that moves with a constant velocity of +5 m/s for a time period of 5 seconds and then accelerates to a final velocity of +15 m/s over the next 5 seconds Now let's consider the same verbal description and the corresponding analysis using kinematic equations. Thus, velocity-time graphs can be used to reveal (or determine) numerical values and relationships between the quantities displacement (d), velocity (v), acceleration (a) and time (t) for any given motion.Įxample Problem - Solution Using Kinematic Equation For example, the velocity of the object at 7 seconds can be determined by reading the y-coordinate value at the x-coordinate of 7 s. Once constructed, the velocity-time graph can be used to determine the velocity of the object at any given instant during the 10 seconds of motion. The above discussion illustrates how a graphical representation of an object's motion can be used to extract numerical information about the object's acceleration and displacement. This is illustrated in the diagram below. As discussed in Lesson 4, the area of a trapezoid can be equated to the area of a triangle lying on top of the area of a rectangle. The area between the line on the graph and the time-axis is representative of the displacement this area assumes the shape of a trapezoid. The displacement of the object can also be determined using the velocity-time graph. Using the velocity-time graph, the acceleration of the object is determined to be 2 m/s 2 during the last five seconds of the object's motion. Thus, the slope (rise/run ratio) is (10 m/s)/(5 s) = 2 m/s 2. This is a total rise of +10 m/s and a total run of 5 s. Between 5 and 10 seconds, the line rises from 5 m/s to 15 m/s and runs from 5 s to 10 s. The slope of the line can be computed using the rise over run ratio. The positively sloped (i.e., upward sloped) section of the graph depicts a positive acceleration, consistent with the verbal description of an object moving in the positive direction and speeding up from 5 m/s to 15 m/s. The horizontal section of the graph depicts a constant velocity motion, consistent with the verbal description. Such a verbal description of motion can be represented by a velocity-time graph. In this part of Lesson 6, we will investigate the relationships between these two methods.Ĭonsider an object that moves with a constant velocity of +5 m/s for a time period of 5 seconds and then accelerates to a final velocity of +15 m/s over the next 5 seconds. Thus, there are now two methods available to solve problems involving the numerical relationships between displacement, velocity, acceleration and time. In Lesson 6, the focus has been upon the use of four kinematic equations to describe the motion of objects and to predict the numerical values of one of the four motion parameters - displacement (d), velocity (v), acceleration (a) and time (t). Thus, velocity-time graphs can be used to determine numerical values and relationships between the quantities displacement (d), velocity (v), acceleration (a) and time (t). In that Lesson, it was emphasized that the slope of the line on a velocity-time graph is equal to the acceleration of the object and the area between the line and the time axis is equal to the displacement of the object. Lesson 4 of this unit at The Physics Classroom focused on the use of velocity-time graphs to describe the motion of objects.
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