WMC 2018 Pursuit - Pack 2, A2

Calculus Level 2

Point P P starts moving on the x x -axis at time t = 0 t=0 . Its position s s is given by s ( t ) = ( t − 8 ) 2 s(t)=(t-8)^2 . At what time t t will P P have travelled 548 548 units?

WMC Pursuit Questions


The answer is 30.

Julian Yu by Julian Yu , 19, Philippines

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1 solution

Tom Engelsman
Oct 6, 2018

At t = 0 t=0 , the particle's position is s ( 0 ) = ( 0 − 8 ) 2 = 64 s(0) = (0-8)^2 = 64 , or the point P ( 64 , 0 ) P(64,0) . When it has travled 548 additional units, the time computes to:

548 = 64 + ( t − 8 ) 2 ⇒ 484 = ( t − 8 ) 2 ⇒ 22 = t − 8 ⇒ t = 30 . 548 = 64 + (t-8)^2 \Rightarrow 484 = (t-8)^2 \Rightarrow 22 = t-8 \Rightarrow \boxed{t = 30}.

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