Answer:
Step-by-step explanation:
when s(t)=0
t^4-20t^2=0
t^2(t^2-20)=0
[tex]t^{2} (t+2\sqrt{5} )(t-2\sqrt{5} )=0\\t=0,-2\sqrt{5} ,2\sqrt{5} \\so particle passes through origin when t=0,-2\sqrt{5} and 2\sqrt{5} \\\frac{x}{y} \frac{ds}{dt} =4t^3-40t\\when particle is motionless \frac{ds}{dt}=0\\4t^3-40t=0\\4t(t^2-10)=0\\t(t+\sqrt{10} )(t-\sqrt{10} )=0\\particle is motionless when t=0,-\sqrt{10} ~or~\sqrt{10}[/tex]
