Question 1

A particle moves in three dimensions with position vector $$\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}. $$Which of the following correctly expresses the instantaneous velocity vector $$\vec{v} in $$terms of the position components?

Accepted Answer

$$\vec{v} = \frac{d\vec{r}}{dt} = \frac{dx}{dt}\hat{i} + \frac{dy}{dt}\hat{j} + \frac{dz}{dt}\hat{k}$$

Question 2

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. $$Neglecting air resistance, how long does it take to hit the ground?

Accepted Answer

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

Question 3

Which of the following best describes the acceleration of a particle moving at constant speed along a curved path?

Accepted Answer

The acceleration is nonzero and points toward the center of curvature.

Question 4

A car rounds a curve at constant speed. Which of the following statements is true?

Accepted Answer

The car is accelerating because its velocity vector is changing direction.

Question 5

Which equation gives the $$y-$$position of a projectile as a function of time $$t$$, if it is launched from $$y_0$$ with initial vertical velocity $$v_{0y}$$ and acceleration $$-g$$?

Accepted Answer

$$y = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 6

Two identical balls are released from the same height at the same time: one is dropped vertically, and the other is shot horizontally. Neglecting air resistance, which ball hits the ground first?

Accepted Answer

They both hit at the same time.

Question 7

Which of the following is the correct formula for the magnitude of the velocity vector $$\vec{v} in $$three dimensions?

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$ + v_z^2$}$$

Question 8

A force is best described as:

Accepted Answer

An interaction between two objects or between an object and its environment.

Question 9

Which of the following is a correct statement about the net force acting on an object?

Accepted Answer

The net force is the vector sum of all forces acting on the object.

Question 10

If you push against a wall and do not move, which force prevents you from passing through the wall?

Accepted Answer

The normal force exerted by the wall.

Question 11

Which of the following is a field (long-range) force?

Accepted Answer

Gravitational force.

Question 12

A particle moves such that its velocity changes in both magnitude and direction. Which of the following is true about its acceleration?

Accepted Answer

The particle has a nonzero acceleration.

Question 13

Which of the following best describes the difference between kinematics and dynamics?

Accepted Answer

Kinematics describes motion; dynamics explains what causes motion.

Question 14

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

Accepted Answer

$$v_{0y} = v_0$ \sin 	heta$$

Question 15

Which of the following is the correct expression for the average acceleration vector $$\vec{a}_{av}$$ over a time interval $$\Delta t$$?

Accepted Answer

$$\vec{a}_{av} = \frac{\Delta \vec{v}}{\Delta t}$$

Question 16

A ball is thrown horizontally from a cliff. Which of the following statements is true about its horizontal velocity (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant.

Question 17

Which of the following is a correct adaptation of the equation of motion to find the $$x-$$position of a projectile (assuming $$x_0 = 0$ and constant velocity in x$)?

Accepted Answer

$$x = v_{0x} t$$

Question 18

Which of the following is a contact force?

Accepted Answer

Friction force.

Question 19

A particle's position is given by $$\vec{r}(t) = (2t)\hat{i} + (3t^2$)\hat{j}. $$What is the particle's velocity at $$t = 1 s$$?

Accepted Answer

$$\vec{v}(1) = 2\hat{i} + 6\hat{j}$$

Kinematics in Two and Three Dimensions: Vectors, Motion, and Forces

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