The position of a nanoparticle as a function of time is x(t)= t² - t - 6,where x is measured in meters,t is measured in seconds and t 0.What is the minimum value of the nanoparticle's position? A)6.00 m B)-6.00 m C)6.25 m D)-6.25 m E)The nanoparticle does not have a minimum value for its position for t0.

Question

The position of a nanoparticle as a function of time is x(t)= t² - t - 6,where x is measured in meters,t is measured in seconds and t > 0.What is the minimum value of the nanoparticle's position? A)6.00 m B)-6.00 m C)6.25 m D)-6.25 m E)The nanoparticle does not have a minimum value for its position for t>0.

Quizplus · Accepted Answer

To find the minimum value of the nanoparticle's position, we can take the derivative of x(t) with respect to t and set it equal to zero. x'(t) = ² - 1 Setting x'(t) = 0 and solving for t, we get t = ². Substituting this value of t back into the original equation for x(t), we get the minimum value of the nanoparticle's position: x(²) = ² * ² - ² - 6 = -6.25 m Therefore, the answer is D: -6.25 m.

The Position of a Nanoparticle as a Function of Time