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

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

Power rule of derivation:

$\overline{){\mathbf{\int}}{{\mathit{x}}}^{{\mathit{n}}}{\mathbf{}}{\mathit{d}}{\mathit{t}}{\mathbf{=}}\frac{\mathbf{1}}{\mathit{n}\mathbf{+}\mathbf{1}}{{\mathit{x}}}^{\mathit{n}\mathbf{+}\mathbf{1}}}$

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

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

$\stackrel{\mathbf{\rightharpoonup}}{\mathbf{r}}\mathbf{}\mathbf{=}[\left(0.280\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.\right)t+\left(0.0360\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{${s}^{2}$}\right.\right){t}^{2}]\hat{\mathbf{i}}\mathbf{}\mathbf{+}\mathbf{}(0.0190\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{${s}^{3}$}\right.){\mathbf{t}}^{\mathbf{3}}\mathbf{}\hat{\mathbf{j}}$

Part A

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

a. vx(t)=(0.0720m/s^{2})t

b. vx(t)=0.280m/s

c. vx(t)=0.280m/s+(0.0720m/s^{2})t

d. vx(t)=(0.280m/s)t+(0.0720m/s^{2})t^{2}

Part B

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

a. vy(t)=(0.0570m/s^{3})t

b. vy(t)=(0.0570m/s^{3})t^{2}

c. vy(t)=(0.0570m/s^{2})t^{2}

d. vy(t)=(0.0570m/s^{3})t+(0.0720m/s^{2})t^{2}

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 =

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Instantaneous Velocity in 2D concept. You can view video lessons to learn Instantaneous Velocity in 2D. Or if you need more Instantaneous Velocity in 2D practice, you can also practice Instantaneous Velocity in 2D practice problems.