The position of an object as a function of time is given by x= bt + ct 3 , where

Question

The position of an object as a function of time is given by x= bt + ct3, where b = 1.50 m/s and c = 0.640m/s3.  To study the limiting process leading to thedefinition of instantaneous velocity, calculate the averagevelocity of the object over time intervals from (a) 1.00 s to 3.00s, (b) 1.50 s to 2.50 s, and (c) 1.95 s to 2.05 s.  Find theinstantaneous velocity as a function of time bydifferentiating. The position of an object as a function of time is given by x= bt + ct3, where b = 1.50 m/s and c = 0.640m/s3.  To study the limiting process leading to thedefinition of instantaneous velocity, calculate the averagevelocity of the object over time intervals from (a) 1.00 s to 3.00s, (b) 1.50 s to 2.50 s, and (c) 1.95 s to 2.05 s.  Find theinstantaneous velocity as a function of time bydifferentiating.

Explanation / Answer

a-x(at t=1s)=1.5+0.64=2.14

x(at t=3s)=7.5+17.28=24.78

v=dx/dt=(24.78-2.14)/(3-1)=

=11.32 m/s

b- v=(13.75-4.41)/2.5-1.5=9.34

c- v=(8.58-7.67)/0.1=9.18

d-v=b+3ct^2

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