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04Rectilinear Motion - RECTILINEAR MOTION Velocity and...

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R ECTILINEAR M OTION Velocity and Acceleration Calculus is most useful when we apply meanings of the derivative other than just the slope of a tangent to a curve. If we have an object moving along a straight line we call this motion rectilinear motion. To model this, we consider a horizontal line with distances to right of the origin as positive and distances to the left of the origin as negative. 0 - ç ===== ==== è + Let f be a function that relates the distance s from 0 and time t , and then we can write ) ( t f s = , where s (displacement) could be the number of meters travelled from 0 in t seconds. ime change ce s changeindi velocity int tan = Eg. If you drive 30 km in 20 min, your velocity over the 30km is h km hr km km / 90 3 / 1 30 min 20 30 = = Of course, this is average velocity, you probably weren’t going 90km/h the whole time. We are more interested in instantaneous velocity . So, to define the velocity of an object at a time 0 t to t t + 0 and let 0 t . Then if the distance travelled by time 0 t is ) ( 0 t f
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