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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