Question

Which is/are correct?

• A. If velocity of a body changes, it must have some acceleration
• B. If speed of a body changes, it must have some acceleration
• C. If body has acceleration, its speed must change
• D. If body has acceleration, its speed may change

Answer 1

Answer: (A), (B), (D)

a, b, d

Answer 2

• a. If velocity of a body changes, it must have some acceleration

  Acceleration is defined as the rate of change of velocity. If the velocity vector ($\vec{v}$) changes (either its magnitude, its direction, or both), then its rate of change ($d\vec{v}/dt$) is non-zero, which means there must be acceleration ($\vec{a} \neq 0$). This statement is correct.

• b. If speed of a body changes, it must have some acceleration

  Speed is the magnitude of the velocity vector ($|\vec{v}|$). If the speed changes, it means the magnitude of the velocity vector is changing. If the magnitude of the velocity vector changes, then the velocity vector itself must change. As established in (a), if the velocity changes, there must be acceleration. This statement is correct.

• c. If body has acceleration, its speed must change

  Acceleration means that the velocity vector is changing. However, the change in velocity does not necessarily mean a change in speed. For example, in uniform circular motion, a body moves with constant speed (magnitude of velocity is constant), but its direction changes continuously. Since the direction of velocity changes, the velocity vector itself changes, and thus there is a non-zero acceleration (centripetal acceleration). In this case, the body has acceleration, but its speed does not change. Therefore, speed does not must change. This statement is incorrect.

• d. If body has acceleration, its speed may change

  As discussed in (c), if a body has acceleration, its velocity is changing. This change in velocity can involve a change in its magnitude (speed) or only a change in its direction, or both.

  • If the acceleration has a component along the direction of motion (tangential acceleration), the speed will change (increase if parallel, decrease if anti-parallel).
  • If the acceleration is perpendicular to the direction of motion (centripetal acceleration), the speed will remain constant, but the direction will change.

  Since speed can change (e.g., a car speeding up in a straight line), this statement is true. This statement is correct.

Based on the analysis, statements a, b, and d are correct.