Conceptual freshman year physics question about acceleration A particle moves along the x-axis. 
When its acceleration is positive,
A. its velocity must be positive
B. it must be speeding up
C. it must be slowing down
D. its velocity must be negative
E. none of the above is always true
The answer to this is $E$, but according to the analysis I've done if the velocity is positive according to formula $a=v/t$,
positive velocity means positive acceleration according to the formula.
Can anybody explain why the answer is given as  $E$?
 A: Two examples should illustrate why answer "E" is the correct answer.
When you work a physics problem, you get to decide which direction is positive.  Accordingly, when you are driving down the road, it is valid to state that the direction that is in front of your car is the positive direction.
Example 1: You are starting from the "x=0" position, and the stop light turns green.  As you press the accelerator pedal, your velocity is positive, you are speeding up, and your acceleration is positive.
Example 2: You are at position x=100 m, and you are traveling in the reverse direction (negative x direction; you are backing up) at 10 m/s.  For whatever reason, you put your automatic transmission into "drive" and press on the accelerator pedal.  At that point, your velocity is negative, you are slowing down, and your acceleration is positive.
In both examples, acceleration is positive, but that is the ONLY thing that the two examples have in common.
A: A simple example that shows why E is the correct option is the following:
Consider a particle moving along x-axis with negative velocity. Now since the acceleration is positive, the speed initially decreases to zero and then increases again. 
A. Isn’t true as our initial velocity is negative. 
B. Isn’t true as we are initially slowing down. 
C. Isn’t true as after speed reaches zero, we’re speeding up. 
D. Isn’t true as the acceleration is positive, we will eventually reach positive velocity (speeding up regime). 
