posted by jack .
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.