An object moves along a coordinate axis so that its position at time t is given by s(t)=t3. Estimate its instantaneous velocity
at time t=2 by computing its average velocity over the time interval [2,2.001].
1 answer:
If the position at time <em>t</em> is
<em>s(t)</em> = (1 m/s³) <em>t</em> ³
then the average velocity over <em>t</em> = 2 s and <em>t</em> = 2.001 s is
<em>v</em> (ave) = (<em>s</em> (2.001 s) - <em>s</em> (2 s)) / (2.001 s - 2 s)
<em>v</em> (ave) = ((1 m/s³) (2.001 s)³ - (1 m/s³) (2 s)³) / (2.001 s - 2 s)
<em>v</em> (ave) ≈ (8.01201 m - 8 m) / (0.001 s)
<em>v</em> (ave) ≈ 12.006 m/s
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