Calculus Review Question

[calcap]

 

[Deleted member 4993]

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[HallsofIvy]

This is a differential equation so I assume you have at least taken a Calculus course. You are told that \(\displaystyle \frac{dx}{dt}= 3 sin(2t)\) so what is x(t)? You are told that \(\displaystyle \frac{dy}{dt}= \sqrt{2}t- 2 sin(t)\) so what is y(t)?

 

[nasi112]

speed [MATH]= v_x = \frac{dx}{dt} = 3\sin 2t[/MATH]
when [MATH]t = 5 \ s, v_x = \ ?[/MATH] (this will be the x-components of the speed)

Do the same for [MATH]v_y = \frac{dy}{dt}[/MATH]
Then, the speed vector is

[MATH]v_x i + v_y j[/MATH]