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 B) negative and negative c) negative and positive D) negative and zero E) positive and zero
If a particle's speed increase over a time period this means that it has acceleration, therefore you can rule out answer choices D and E. If a particle's speed increases, its' acceleration can not be negative, and therefore must be positive. Therefore, you can rule out A and B. This leaves answer choice C as the best answer choice.
If the speed is increasing, the acceleration cannot be zero.
If the particle also remains moving along the x-axis, the velocity and acceleration must have the same direction.
The statement that the velocity and acceleration MUST be in the SAME DIRECTION is not correct. A particle can have an initial velocity in one direction and have an acceleration in another. Over time, the particle's velocity will not be in the opposite direction of the acceleration, but will be in the direction of the acceleration. This question is basically a question asking do you understand Newton's second law.
answer is positve and postive negative and negative
To determine the relationship between the velocity and acceleration of a moving particle, we need to consider the signs of both quantities.
Velocity is a vector quantity that describes the rate at which an object changes its position. It has both magnitude and direction. Acceleration, on the other hand, is the rate at which the velocity of an object changes. It is also a vector quantity, with magnitude and direction.
Given that the speed of the particle is increasing as it moves along the x-axis, we can infer that the velocity is positive, as the particle is moving in the positive x-direction.
Now, let's consider the possible combinations of signs for the velocity and acceleration:
a) Positive and negative: If the velocity is positive (moving in the positive x-direction) and the acceleration is negative, it means the particle is slowing down or decelerating in the positive x-direction. This would not be the case since the particle's speed is increasing.
b) Negative and negative: If both velocity and acceleration are negative, it means the particle is moving in the negative x-direction, and its speed is decreasing. Again, this contradicts the given information that the particle's speed is increasing.
c) Negative and positive: If the velocity is negative (moving in the negative x-direction) and the acceleration is positive, it means the particle is speeding up while moving in the negative x-direction. This is possible, but in this case, the speed of the particle would be decreasing, not increasing as stated.
d) Negative and zero: If the velocity is negative, but the acceleration is zero, it means the particle is moving at a constant speed in the negative x-direction. Again, this does not align with the given information that the particle's speed is increasing.
e) Positive and zero: If the velocity is positive, and the acceleration is zero, it means the particle is moving at a constant speed in the positive x-direction. This contradicts the information that the particle's speed is increasing.
Based on the above analysis, the only possible combination of signs that matches the given condition is:
a) Positive and negative