A particle has velocity v(t)=2t²−kt+8 m/s. If it becomes instantaneously at rest at exactly one time and k is positive, find k.
Physics · Mathematical tools and vector · Quadratic Equation
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Question

A particle has velocity v(t)=2t²−kt+8 m/s. If it becomes instantaneously at rest at exactly one time and k is positive, find k.

G1 Physics · Accepted Answer

Exactly one time means the quadratic has equal roots. D=(−k)²−4(2)(8)=k²−64=0. Hence k=±8; given k>0, k=8.