Question

If the positive direction is downward, which situation involves negative velocity and zero acceleration?
a) A rocket slowing down as it moves upwards
b) A rocket moving downward at a constant speed
c) A rocket moving upward at a constant speed
d) A rocket speeding up as it moves upwards

Answer 1

Velocity of a particle is defined as the change in position with respect to time. The velocity of the particle is said to be positive or negative depending on the direction and the convention taken for the direction. The acceleration is the change in velocity of the particle with time. Hence using this information, we can select the correct alternative such that it satisfies the condition mentioned in the question.
Formula used:
$v=\dfrac{\Delta x}{t}$

Complete answer:
In the question it is given to us that the upward direction by convention is to be taken as negative. Hence as a body moves upwards its change in position with respect to some reference point will be negative.
Let us say for such a convention, a body moves upwards with respect to some reference point. The change in position i.e., $\Delta x$ of the body will be negative. If the body changes its position in this direction in time ‘t’, then the velocity ‘v’ of the body is equal to,
$v=\dfrac{-\Delta x}{t}$
The acceleration of any body is defined as the rate of change of velocity. If the body moves with a constant speed, the acceleration of the body is zero as there is no change in velocity.
Hence from the above conclusions drawn, the rocket will have a negative velocity and zero acceleration only if the rocket is moving upward at a constant speed.

Therefore, the correct answer of the above question is option c.

Note:
It is to be noted that the negative velocity means that the body is moving in a negative direction (as per the convention) and does not mean that the velocity is small. The direction is a matter of convention. It is also to be noted that negative acceleration also means the same, but velocity of the body will decrease.