Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
The velocity is defined by:
[tex]v=\frac{dx}{dt}[/tex]where x is the position of the particle and t is the time.
Plugging the position function given we have that the velocity is:
[tex]\begin{gathered} v=\frac{dx}{dt} \\ =\frac{d}{dt}(24t-2t^3) \\ =24-6t^2 \end{gathered}[/tex]Hence the velocity is given by the function:
[tex]v=24-6t^2[/tex]to determine the isntant when the velocity is zero we equate its expression to zero and solve for t:
[tex]\begin{gathered} 24-6t^2=0 \\ 6t^2=24 \\ t^2=\frac{24}{6} \\ t^2=4 \\ t=\pm\sqrt[]{4} \\ t=\pm2 \end{gathered}[/tex]Since time is always positive we conclude that the velocity is zero at t=2 s.
Now that we know at which instant the velocity is zero we need to remember that the acceleration is defined as:
[tex]a=\frac{dv}{dt}[/tex]then we have that:
[tex]\begin{gathered} \frac{dv}{dt}=\frac{d}{dt}(24-6t^2) \\ =-12t \end{gathered}[/tex]hence the acceleration is:
[tex]a=-12t[/tex]Plugging the value we found for the time we have that:
[tex]a(2)=-12(2)=-24[/tex]Therefore the acceleration of the particle when its velocity is zero is -24 meters per second per second.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.