# Problem: The position of a squirrel running in a park is given by r⇀ =[0.280 mst + 0.0360 ms2t2]i^ + (0.0190 ms3)t3 j^Part AWhat is υx(t), the x-component of the velocity of the squirrel, as function of time?a. vx(t)=(0.0720m/s2)tb. vx(t)=0.280m/sc. vx(t)=0.280m/s+(0.0720m/s2)td. vx(t)=(0.280m/s)t+(0.0720m/s2)t2     Part BWhat is υy(t), the y-component of the velocity of the squirrel, as function of time?a. vy(t)=(0.0570m/s3)tb. vy(t)=(0.0570m/s3)t2c. vy(t)=(0.0570m/s2)t2d. vy(t)=(0.0570m/s3)t+(0.0720m/s2)t2Part CAt 4.66 s, how far is the squirrel from its initial position?Express your answer to three significant figures and include the appropriate units.r =Part DAt 4.66 s, what is the magnitude of the squirrel's velocity?Express your answer to three significant figures and include the appropriate units.v =Part EAt 4.66 s, what is the direction (in degrees counterclockwise from +x-axis) of the squirrel's velocity?Express your answer to three significant figures and include the appropriate units.θ =

###### FREE Expert Solution

In this problem, the position function has time raised to a given power. We are also asked for the velocity function. Thus, we know that this is a kinematics problem with calculus.

For motion with calculus problems, the following relation is important.

Motion with Calculus

$\mathbit{P}\begin{array}{c}{\mathbf{←}}\\ {\mathbf{\to }}\end{array}\underset{\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}}{\overset{{\mathbf{\int }}{\mathbit{d}}{\mathbit{t}}}{\mathbit{V}}}\begin{array}{c}{\mathbf{←}}\\ {\mathbf{\to }}\end{array}\mathbit{A}$

Power rule of derivation:

$\overline{)\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}\mathbf{\left(}{\mathbit{x}}^{\mathbit{n}}\mathbf{\right)}{\mathbf{=}}{\mathbit{n}}{{\mathbit{x}}}^{\mathbit{n}\mathbf{-}\mathbf{1}}}$

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###### Problem Details

The position of a squirrel running in a park is given by

Part A
What is υx(t), the x-component of the velocity of the squirrel, as function of time?

a. vx(t)=(0.0720m/s2)t
b. vx(t)=0.280m/s
c. vx(t)=0.280m/s+(0.0720m/s2)t
d. vx(t)=(0.280m/s)t+(0.0720m/s2)t2

Part B
What is υy(t), the y-component of the velocity of the squirrel, as function of time?

a. vy(t)=(0.0570m/s3)t
b. vy(t)=(0.0570m/s3)t2
c. vy(t)=(0.0570m/s2)t2
d. vy(t)=(0.0570m/s3)t+(0.0720m/s2)t2

Part C
At 4.66 s, how far is the squirrel from its initial position?
Express your answer to three significant figures and include the appropriate units.

r =

Part D
At 4.66 s, what is the magnitude of the squirrel's velocity?
Express your answer to three significant figures and include the appropriate units.

v =

Part E
At 4.66 s, what is the direction (in degrees counterclockwise from +x-axis) of the squirrel's velocity?
Express your answer to three significant figures and include the appropriate units.

θ =