1. throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:

A. positive and negative, respectively
B. negative and positive, respectively
C. negativa and negative, respectively
D. negative and zero, respectively
E. positive and zero, respectively

2. An object is thrown vertically upward. While it is rising:

A. its velocity and acceleration are both upward
B. its velocity is upward and its acceleration is downward
C. its velocity and acceleration are both downward
D. its velocity is downward and its acceleration is upward
E. its velocity and acceleration are both decreasing

on the first, the direction of travel is not specified, so it could be either.

On the second, gravity is always acting downward, is it not?

1 = A

1. The correct answer is A. positive and negative, respectively. As the speed of a particle increases along the x-axis, its velocity can be positive (indicating movement in the positive x-axis direction) while its acceleration is negative (indicating a decrease in velocity or deceleration).

2. The correct answer is B. Its velocity is upward and its acceleration is downward. When an object is thrown vertically upward, its velocity is directed upward initially. However, due to the force of gravity acting on the object, its acceleration is directed downward.

1. In order to determine the relationship between the speed, velocity, and acceleration of a particle as it moves along the x-axis, we need to understand the definitions of these terms.

- Speed: This refers to the magnitude of the particle's motion, regardless of its direction. It tells us how fast the particle is moving. Speed is always positive since it only considers the magnitude of the motion.

- Velocity: This refers to both the magnitude and direction of the particle's motion. Velocity tells us the speed of the particle and the direction in which it is moving. It can be positive (indicating motion in the positive x-direction) or negative (indicating motion in the negative x-direction).

- Acceleration: This refers to the rate at which the velocity of the particle is changing. It tells us how quickly the velocity is increasing or decreasing. Acceleration can be positive (indicating an increase in velocity) or negative (indicating a decrease in velocity).

Now, let's analyze the given options:

A. Positive velocity and negative acceleration: This situation occurs when the particle is moving in the positive x-direction with increasing speed. However, its acceleration is negative because it is slowing down.

B. Negative velocity and positive acceleration: This situation occurs when the particle is moving in the negative x-direction with decreasing speed. However, its acceleration is positive because it is speeding up.

C. Negative velocity and negative acceleration: This situation occurs when the particle is moving in the negative x-direction and slowing down. Both velocity and acceleration have the same sign.

D. Negative velocity and zero acceleration: This situation occurs when the particle is moving at a constant velocity in the negative x-direction. There is no change in its velocity since acceleration is zero.

E. Positive velocity and zero acceleration: This situation occurs when the particle is moving at a constant velocity in the positive x-direction. There is no change in its velocity since acceleration is zero.

From the given options, it is clear that the correct answer is option A: positive velocity and negative acceleration.

2. When an object is thrown vertically upward, we need to consider the changes in its velocity and acceleration.

- Velocity: Initially, when the object is thrown upward, its velocity is positive since it moves in the positive y-direction. However, as the object rises higher, its velocity decreases until it reaches its maximum height, where its velocity becomes zero. After that, the object starts to fall downward, and its velocity becomes negative as it moves in the negative y-direction.

- Acceleration: The acceleration due to gravity is always directed downward (negative) irrespective of the direction of motion. Hence, the acceleration of the object is always downward, regardless of whether it is rising or falling.

Based on the above explanations, the correct answer is option B: its velocity is upward, and its acceleration is downward while it is rising.