A dog running in an open field has components of velocity v_x = 2.6 m/s and v_y = −1.8 m/s at t1 = 10.0 s. For the time interval from t₁ = 10.0 s to t₂ = 20.0 s, the average acceleration of the dog has magnitude 0.45 m/s² and direction 31.0° measured from the +x–axis toward the +y–axis. At t₂ = 20.0 s, what are the x- and y-components of the dog's velocity?

The position of a squirrel running in a park is given by $\(\vec{r}\) = \(\left\)[ (0.280~\(\mathrm{m/s}\))t + (0.0360~\(\mathrm{m/s^2}\))t^2 \(\right\)] \(\hat{i}\) + (0.0190~\(\mathrm{m/s^3}\))t^3 \(\hat{j}\)$. At $t=5.00s$, how far is the squirrel from its initial position?

The position of a squirrel running in a park is given by $\(\vec{r}\) = \(\left\)[ (0.280~\(\mathrm{m/s}\))t + (0.0360~\(\mathrm{m/s^2}\))t^2 \(\right\)] \(\hat{i}\) + (0.0190~\(\mathrm{m/s^3}\))t^3 \(\hat{j}\)$. (a) What are $v_x\left(t\right)$ and $v_y\left(t\right)$, the $x$-and $y$-components of the velocity of the squirrel, as functions of time?

A web page designer creates an animation in which a dot on a computer screen has position $\overrightarrow{r}=[4.0\mathrm{cm}+\left(2.5{\text{ cm/s}}^2\right)t^2]i+\left(5.0\mathrm{cm/s}\right)tj$. Find the magnitude and direction of the dot's average velocity between $t=0$ and $t=2.0s$.

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the velocity and acceleration vectors of the bird as functions of time.