Question

A particle moving along a line has position s(t) = t^4 − 20t^2 m at time t seconds. Determine: (a)- At which times does the particle pass through the origin? (b)- At which times is the particle instantaneously motionless.

Answer 1

Answer:

Step-by-step explanation:

when s(t)=0

t^4-20t^2=0

t^2(t^2-20)=0

$t^{2} (t+2\sqrt{5} )(t-2\sqrt{5} )=0\\t=0,-2\sqrt{5} ,2\sqrt{5} \\so particle passes through origin when t=0,-2\sqrt{5} and 2\sqrt{5} \\\frac{x}{y} \frac{ds}{dt} =4t^3-40t\\when particle is motionless \frac{ds}{dt}=0\\4t^3-40t=0\\4t(t^2-10)=0\\t(t+\sqrt{10} )(t-\sqrt{10} )=0\\particle is motionless when t=0,-\sqrt{10} ~or~\sqrt{10}$