A particle has velocity v(t)=t²−6t+k m/s. If its velocity never becomes zero for any real time, which condition must k satisfy?
Physics · Mathematical tools and vector · Quadratic Equation
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Question

A particle has velocity v(t)=t²−6t+k m/s. If its velocity never becomes zero for any real time, which condition must k satisfy?

G1 Physics · Accepted Answer

Velocity never becomes zero when t²−6t+k=0 has no real roots. Therefore D<0: 36−4k<0 ⇒ k>9.