To measure a velocity, it is necessary to know both a distance Δ s and a time Δ t, however small.Ī body in motion is in motion during every interval of time in which it moves. It is the limit of a sequence of velocities as Δ t approaches 0 it is purely logical it can never be observed or measured. Instantaneous velocity is not an ordinary velocity. And let 10:05 AM correspond to t = 0.Ī) What is the instantaneous velocity at 10:05 AM? Answer.ī) What is the instantaneous velocity at 10:15 AM? Let t be measured in minutes and s in meters. Let the following be the equation of motion:
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The instantaneous velocity is the value of the slope of the tangent line at t.Įxample 1. The graph was not a straight line.įor any equation of motion s( t), by the instantaneous velocity at time t- v( t)-we mean the limit of the average velocity,, between t and t + Δ t, as Δ t approaches 0. During that acceleration, the velocity was not constant. That is not a realistic picture, of course, because at 0 seconds the velocity is surely not 22 meters/sec. In each 1 second of time, the particle moves a distance of 22 meters.
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For the slope of that line-22-is rate of change of s with respect to t, which by definition is the velocity. Then at every instant of time, the velocity, v( t), is 22 m/sec. In other words, if the equation of motion is Now, if the particle moves with constant velocity-which is called uniform motion-then we don't need calculus. When we know s( t), we have what is called the equation of motion. Then to each value of t there will correspond a distance s, which will be a function of t:
![motion 5.4.1 free motion 5.4.1 free](https://assets.adidas.com/images/w_600,f_auto,q_auto/ea28e440932b48b4926aac7c01553909_9366/AEROREADY_Flow_Primeblue_Pants_Blue_GP5403.jpg)
O NE OF THE most important applications of calculus is to motion in a straight line, which is called rectilinear motion.Ĭonsider a particle moving in a straight line from a fixed point O to a given point P, and let t be the time elapsed.
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