Conceptual acceleration, velocity, and position
Determine if the following statements are true or false. Remember that for a statement to be true it must be true in all cases.
a)If the velocity of an object is zero, then the acceleration of an object must also be zero.
b)If the initial velocity of an object is zero, then the initial speed of the object must be zero.
c)If the average velocity of an object is zero, then the average speed of the object must also be zero.
d)If the initial speed of an object is zero, then the initial position of the object must be the origin.
e)The acceleration of an object can be non-zero when the speed of the object is constant.
The Attempt at a Solution
a)True - if the velocity of the object is zero, and acceleration is the derivative of velocity, then both velocity and acceleration are zero.
b)False - initial velocity has direction while initial speed has none. the initial velocity could be zero because its components are in opposing directions and are equal. However, if this were true, then speed would be non-zero because one of the components would no longer be negative.
c)False - the average velocity is the total displacement over total time. Average speed is the total distance traveled over total time. Average speed does not take into account the direction of the position vector, only its magnitude.
d)False - even though an object may be at rest to begin with, this does not necessarily place it at the origin. This varies from problem to problem.
e)False - if speed is constant then that means that velocity must be constant. This means that acceleration is zero since velocity is unchanging.
I don't understand where I am going wrong in my thought process. I have been going through this problem so many times it's ridiculous, though it should seem simple. Am I missing something obvious?