A dust mote moves along a line. Its position is described bythe function x(t)=12

Question

A dust mote moves along a line. Its position is described bythe function x(t)=12-30t-6t2 where position is in metersand time is in seconds. (a) what is the particle's at t=7s? (b)what is the motes instantaneous velocity at t=7s? (c) what is themote's instantaneous acceleration at t=7 s? Express the answer tothe nearest integer. Will someone please explain stepe by step how to do thisproblem please? A dust mote moves along a line. Its position is described bythe function x(t)=12-30t-6t2 where position is in metersand time is in seconds. (a) what is the particle's at t=7s? (b)what is the motes instantaneous velocity at t=7s? (c) what is themote's instantaneous acceleration at t=7 s? Express the answer tothe nearest integer. Will someone please explain stepe by step how to do thisproblem please?

Explanation / Answer

a) x(t=7s) = 12-30*7s - 6*(7s)2 = -454m the particle is at -453.58m location b) v(t) = dx(t)/dt = -30 - 12t speed at t=7s is: v(7s) = -30-12*7s = -114m/s c) acceleration a(t) = dv(t)/dt = -12 a(t=7s) = -12m/s2

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