A web page designer creates an animation in which a dot on a computer screen has a position of
r = [4.2 + 3t^2]i + 5.4tj.
find the average velocity of the dot between t=0 and t = 2
Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.
I know you take the derivative of the function and plug in 0 and 2
t(0) = 0i + 5.4j
t(2) = 12i + 5.4 j
I'm stuck here though and don't know how to get the x AND y components
r = [4.2 + 3t^2]i + 5.4tj.
find the average velocity of the dot between t=0 and t = 2
Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.
I know you take the derivative of the function and plug in 0 and 2
t(0) = 0i + 5.4j
t(2) = 12i + 5.4 j
I'm stuck here though and don't know how to get the x AND y components
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Not my strongest area of ability, but I think I can help
You seem to have the correct means of going about it.
With respect to t
r(t) = [4.2 + 3t^2]i + 5.4tj
r'(t) = 6ti + 5.4j
r'(0) = 6(0)i + 5.4j = 0i + 5.4j
r'(2) = 6(2)i + 5.4j = 12i +5.4j
which is what you have
now just average the i and j terms
so the average velocity is
((0 + 12)/2)i + ((5.4 + 5.4)/2)j = 6i + 5.4j
You seem to have the correct means of going about it.
With respect to t
r(t) = [4.2 + 3t^2]i + 5.4tj
r'(t) = 6ti + 5.4j
r'(0) = 6(0)i + 5.4j = 0i + 5.4j
r'(2) = 6(2)i + 5.4j = 12i +5.4j
which is what you have
now just average the i and j terms
so the average velocity is
((0 + 12)/2)i + ((5.4 + 5.4)/2)j = 6i + 5.4j