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 $t=8.00s$?

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.

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?

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.