The position vector r describes the path of an object moving in the xy-plane. (b) Evaluate the velocity vector and acceleration vector of the object at the given point. Position Vector: r(t) = (¼t³ + 1)i + tj Point: (3, 2)

The position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity vector, speed, and acceleration vector of the object. Position Vector: r(t) = ⟨t - sin t, 1 - cos t⟩ Point: (π, 2)

In the following exercise, the position vector r describes the path of an object moving in the xy-plane.

Position Vector: $r(t)=(6-t) i+t j$

Point: (3, 3)

Find the velocity vector, speed, and acceleration vector of the object.

In the following exercise, the position vector r describes the path of an object moving in the xy-plane.

Position Vector: $r(t)=t^2 i+t j$

Point: (4, 2)

Find the velocity vector, speed, and acceleration vector of the object.

The position vector r describes the path of an object moving in the xy-plane. (b) Evaluate the velocity vector and acceleration vector of the object at the given point. Position Vector: r(t) = 2 cos ti + 2 sin tj Point: (√2, √2)

The position $\vec{r}$ of a particle moving in the xy plane is given by $\vec{r}=2 t \hat{i}+2 \sin [(\pi / 4 \mathrm{rad} / \mathrm{s}) t \hat{\mathrm{j}}$, where $\vec{r}$ is in meters and t is in seconds.

Calculate the components of the particle's acceleration at t=1.0,2.0, and 3.0 s.

The position $\vec{r}$ of a particle moving in the xy plane is given by $\vec{r}=2 t \hat{i}+2 \sin [(\pi / 4 \mathrm{rad} / \mathrm{s}) t \hat{\mathrm{j}}$, where $\vec{r}$ is in meters and t is in seconds.

Calculate the components of the particle's velocity at t= 1.0,2.0, and 3.0 s. Show that the velocity is tangent to the path of the particle and in the direction the particle is moving at each time by drawing the velocity vectors on the plot of the particle's path in part (a).

The position vector r describes the path of an object moving in the xy-plane. (b) Evaluate the velocity vector and acceleration vector of the object at the given point. Position Vector: r(t) = ti + (-t² + 4) j Point: (1, 3)

The position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity vector, speed, and acceleration vector of the object. Position Vector: r(t) = t²i + tj Point: (4, 2)

The position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity vector, speed, and acceleration vector of the object. Position Vector: r(t) = ⟨e^-t, e^t⟩ Point: (1, 1)

The position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity vector, speed, and acceleration vector of the object. Position Vector: r(t) = 3 cos ti + 2 sin tj Point: (3, 0)

Long flights at midlatitudes in the Northern Henisphere encounter the jet stream. an eastward airflow that can affect a plane's speed relative to Earth's surface. If a pilot maintains a certain speed relative to the air (the plane's airspeed), the speed relative to the surface (the plane's ground speed) is more when the flight is in the direction of the jet stream and less when the flight is opposite the jet stream. Suppose a round-trip flight is scheduled between two cities separated by $5000 \mathrm{~km}$, with the outgoing flight in the direction of the jet stream and the return flight opposite it. The airline computer advises an airspeed of $1000 \mathrm{~km} / \mathrm{h}$, for which the difference in flight times for the outgoing and return flights is $70.0 \mathrm{~min}$. What jet-stream speed is the computer using?

Long flights at midlatitudes in the Northern Hemisphere encounter the jet stream, an eastward airflow that can affect a plane’s speed relative to Earth’s surface. If a pilot maintains a certain speed relative to the air (the plane’s airspeed), the speed relative to the surface (the plane’s ground speed) is more when the flight is in the direction of the jet stream and less when the flight is opposite the jet stream. Suppose a round-trip flight is scheduled between two cities separated by 4000 km, with the outgoing flight in the direction of the jet stream and the return flight opposite it. The airline computer advises an airspeed of 1000 km/h, for which the difference in flight times for the outgoing and return flights is 70.0 min. What jet-stream speed is the computer using?

Long flights at mid-latitudes in the Northern Hemisphere encounter the jet stream, an eastward airflow that can affect a plane's speed relative to Earth's surface. If a pilot maintains a certain speed relative to the air, the speed relative to the surface is more when the flight is in the direction of the jet stream and less when the flight is opposite the jet stream. Suppose a round-trip flight is scheduled between two cities separated by $4000 \mathrm{~km}$, with the outgoing flight in the direction of the jet stream and the return flight opposite it. The airline computer advises an airspeed of $1000 \mathrm{~km} / \mathrm{h}$, for which the difference in flight times for the outgoing and return flights is $100.0 \mathrm{~min}$. What jet-stream speed is the computer using?