p02_019

Fundamentals of Physics,Vol 1 (Chapters 1 - 20)

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19. In this solution, we make use of the notation x ( t ) for the value of x at a particular t .T h u s , x ( t )= 50 t +10 t 2 with SI units (meters and seconds) understood. (a) The average velocity during the Frst 3 s is given by v avg = x (3) x (0) t = (50)(3) + (10)(3) 2 0 3 =80m / s . (b) The instantaneous velocity at time t is given by v = dx/dt =50+20 t , in SI units. At t =3 . 0s , v = 50 + (20)(3 . 0) = 110 m/s. (c) The instantaneous acceleration at time t is given by a = dv/dt =20m / s 2 . It is constant, so the acceleration at any time is 20 m / s 2 . (d) and (e) The graphs below show the coordinate x and velocity v as functions of time, with SI units understood. The dotted line marked (a) in the Frst graph runs from t =0 , x =0to
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Unformatted text preview: (b) is tangent to the x curve at t = 3 . 0 s. Its slope is the instantaneous velocity at t = 3 . 0 s. ............................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . .... .. .. .... . ... .... . ... .... .... ... . .... .. .. .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 2 . 3 . 4 . 100 200 300 400 (a) (b) t x ..................................................................................................................... 1 . 2 . 3 . 4 . 50 100 150 200 t v...
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This document was uploaded on 04/18/2008.

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