Question

Which of the following statements must always be true?
I. If an object’s acceleration is zero, then its speed must remain constant
II. If an object’s acceleration is constant, then it must move in a straight line
III. If an object’s speed remains constant, then its acceleration must be zero
(A) I and II only
(B) I and III only
(C) I only
(D) III only
(E) II and III only

Answer 1

Hint : We need to check the validity of each statement with Newton’s laws of motion. In a circulatory motion, the speed is considered constant but requires a centripetal acceleration to remain in circulatory motion.

Complete step by step answer
To verify each statement, we shall compare them to Newton’s laws of motion. If it does not satisfy the statement, then it is certainly false but if it confirms the statement, it is true. If silent, then we must check through falsity by counter example.
For the first statement, if an object’s acceleration is zero, then its speed must remain constant. According to Newton’s second law, when the acceleration of a body is zero, then no external force is acting on the body. Now, according to Newton’s first law, the velocity of a body is constant (being zero is also being constant) when no net external force acts on it. Hence, statement I is correct
For the second statement, we know that by Newton’s second law, if an object has acceleration, then it has a force. Since forces can be applied to change the direction of motion, then statement II is incorrect.
For statement three, Newton’s law has no direct comment about the object speed with acceleration. But if we consider that an object in rotational motion may have a constant speed, yet has a centripetal acceleration. Hence, the statement three is false.
Thus, the correct option is C.

Note
For clarity, we say that Newton’s law has no direct comment on the speed as relating to acceleration because acceleration is the rate of change of velocity, and not speed. Thus, Newton’s law tells us about the velocity change but doesn’t mention whether or not a constant speed equals a constant velocity. In general, just based on Newton's law only, truth value of statement III cannot be concluded.