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Let s(t) denote the position of a particle in cm after t seconds. Suppose that we are unable to write a formula for s(t), but we know that when t=1 second, the particle has position 5cm and velocity 2cm/s. Use linearization to approximate the location of the particle when t=1.1 secons. 

 Mar 21, 2016
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If we linearize then the change in distance is equal to the velocity times the change in time, so:

 

change in distance = 2*(1.1 - 1) cm  →  0.2 cm

 

location at t = 1.1 s is  therefore 5.2 cm

 Mar 21, 2016

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