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A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(5t). Find the acceleration of the particle when the velocity is first zero. (4 points)

5e

5e2

e

None of these

1 Answer

3 votes

The particle's velocity is given by the derivative of its position:


s'(t)=\ln5t+t\frac5{5t}=\ln5t+1

which will be 0 when


\ln5t+1=0\implies\ln5t=-1\implies5t=e^(-1)\implies t=\frac1{5e}

The acceleration is given by the second derivative, so we have


s''(t)=\frac5{5t}=\frac1t

and at
t=\frac1{5e}, the acceleration will be


s''\left(\frac1{5e}\right)=\frac1{\frac1{5e}}=5e

User Initialxy
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