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

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?

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?

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 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.

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.

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are $a_x\left(t\right)$ and $a_y\left(t\right)$, the $x$- and $y$- components of the car's velocity as functions of time?

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are the magnitude and direction of the car's velocity at $t=8.00s$? (b) What are the magnitude and direction of the car's acceleration at $t=8.00s$?

A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.480 s. Ignore air resistance. Find the height of the tabletop above the floor.

A daring 510 N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. E3.10. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff?

Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy drops downward and reaches the ground in 2.70 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground? Ignore air resistance.

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How much time is required for the football to reach the highest point of the trajectory?

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How high is this point?

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)?

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How far has the football traveled horizontally during this time?

The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0° above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See Nature, Vol. 424, July 31, 2003, p. 509.) What was the takeoff speed for such a leap?