![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, We are only concerned with motion in one dimension. Then you must include on every physical page the following attribution: uniform acceleration How the Kinematic Equations are Related to Acceleration We are studying concepts related to motion: time, displacement, velocity, and especially acceleration. If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The box below provides easy reference to the equations needed. The examples also give insight into problem-solving techniques. In the following examples, we further explore one-dimensional motion, but in situations requiring slightly more algebraic manipulation. (This is why we have reduced speed zones near schools.) For a fixed deceleration, a car that is going twice as fast doesn’t simply stop in twice the distance-it takes much further to stop.The final velocity depends on how large the acceleration is and the distance over which it acts.In addition to being useful in problem solving, the equation v = v 0 + at v = v 0 + at size 12 can produce further insights into the general relationships among physical quantities: Note that the acceleration is negative because its direction is opposite to its velocity, which is positive. To summarize, using the simplified notation, with the initial time taken to be zero,įigure 2.29 The airplane lands with an initial velocity of 70.0 m/s and slows to a final velocity of 10.0 m/s before heading for the terminal. Also, it simplifies the expression for change in velocity, which is now Δ v = v − v 0 Δ v = v − v 0. It also simplifies the expression for displacement, which is now Δ x = x − x 0 Δ x = x − x 0. This gives a simpler expression for elapsed time-now, Δ t = t Δ t = t. That is, t t is the final time, x x is the final position, and v v is the final velocity. We put no subscripts on the final values. That is, x 0 x 0 is the initial position and v 0 v 0 is the initial velocity. When initial time is taken to be zero, we use the subscript 0 to denote initial values of position and velocity. ![]() Since elapsed time is Δ t = t f − t 0 Δ t = t f − t 0, taking t 0 = 0 t 0 = 0 means that Δ t = t f Δ t = t f, the final time on the stopwatch. Taking the initial time to be zero, as if time is measured with a stopwatch, is a great simplification. Notation: t, x, v, aįirst, let us make some simplifications in notation. In this section, we develop some convenient equations for kinematic relationships, starting from the definitions of displacement, velocity, and acceleration already covered. But we have not developed a specific equation that relates acceleration and displacement. We might know that the greater the acceleration of, say, a car moving away from a stop sign, the greater the displacement in a given time. Figure 2.25 Kinematic equations can help us describe and predict the motion of moving objects such as these kayaks racing in Newbury, England.
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