Question 1

A particle moves in the xy-plane such that its position at time $$t is $$given by $$\vec{r}(t) = (4t^2$)\hat{i} + (3t)\hat{j}$$, where $$t is in $$seconds and position is in meters. What is the particle's instantaneous velocity at $$t = 2 s$$?

Accepted Answer

$$\vec{v} = (16)\hat{i} + (3)\hat{j} m/s$$

Question 2

Which of the following correctly expresses the average velocity vector $$\vec{v}_{av}$$ for a particle moving from position $$\vec{r}_1 at $$time $$t_1 to $$position $$\vec{r}_2 at $$time $$t_2$$?

Accepted Answer

$$\vec{v}_{av} = \frac{\vec{r}_2 - \vec{r}_1}{t_2$ - t_1$}$$

Question 3

A ball is thrown horizontally from a cliff with an initial speed $$v_0. $$Ignoring air resistance, which statement is true about the ball's motion?

Accepted Answer

The ball's vertical velocity increases in magnitude due to gravity.

Question 4

A car moves along a curved path at constant speed. What is the direction of its acceleration?

Accepted Answer

Perpendicular to the velocity, toward the center of curvature

Question 5

A projectile is launched with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$v_0$$ \sin 	heta$$

Question 6

A bird flying at 18 m/s, 30° below the horizontal, drops a fish from a height of 16 m above the water. Ignoring air resistance, how long does it take for the fish to hit the water?

Accepted Answer

$$t = \frac{-18 \sin 30^\circ + \sqrt{(18 \sin 30^\$$circ)^2$$ + 2 	imes 9.8 	imes 16}}{9.8}$$

Question 7

A race car travels around a circular track of radius $$R at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{R}$$

Question 8

A person walks east at 2 m/s on a train moving north at 10 m/s. What is the magnitude of the person's velocity relative to the ground?

Accepted Answer

$$\sqrt{10^2$ + 2^2$} = 10.2 m/s$$

Question 9

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. $$What is the time it takes to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 10

A satellite orbits Earth at a radius $$r$$ with period $$T. $$What is its speed?

Accepted Answer

$$v = \frac{2\pi r}{T}$$

Question 11

A car and a truck are moving toward each other on a straight road. The truck moves at 80 m/s and the car at 50 m/s (both speeds relative to the ground). What is the velocity of the truck relative to the car?

Accepted Answer

$$130 m/s$$

Question 12

Which of the following statements about acceleration in circular motion is correct?

Accepted Answer

Acceleration is always perpendicular to velocity.

Question 13

A projectile is launched at $$v_0 = 20$ m/s at 30$$^\circ$$ above the horizontal. What is the horizontal component of its velocity?

Accepted Answer

$$20 \cos 30^\circ$$

Question 14

Two balls, A and B, are dropped from the same height. Ball A is dropped from rest, and ball B is dropped from a moving airplane flying horizontally at constant speed. Ignoring air resistance, which statement is true?

Accepted Answer

Both balls reach the ground at the same time, but B has a greater horizontal velocity.

Question 15

A crate is pushed across a floor with a constant acceleration $$\vec{a} = 5\hat{i} + 3\hat{j} m/s$^2. If $$its initial velocity is $$5\hat{i} m/s$$, what is its velocity after it has been displaced by 10 m in the y-direction?

Accepted Answer

$$\vec{v} = 17.9\hat{i} + 7.75\hat{j} m/s$$

Question 16

Which equation correctly gives the instantaneous velocity vector $$\vec{v} in $$two dimensions?

Accepted Answer

$$\vec{v} = \frac{d\vec{r}}{dt}$$

Question 17

A plane is headed due north at 240 km/h through the air, but the wind is blowing east at 100 km/h. What is the plane's speed relative to the ground?

Accepted Answer

$$260 km/h$$

Question 18

A skier moves over the crest of a snow-covered hill. At the very top (crest), what is the direction of the acceleration vector?

Accepted Answer

Straight down

Question 19

Which of the following is true about the instantaneous velocity vector $$\vec{v}$$ for a particle moving along a curved path?

Accepted Answer

$$\vec{v} is $$always tangent to the path.

Motion in Two Dimensions: Kinematics, Velocity, and Acceleration

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