When a body is said to be accelerating, what can we correctly say about the behaviour of its speed and direction of motion over time?

Introduction / Context:
Acceleration is a fundamental concept in kinematics and dynamics. Many learners initially think of acceleration only as speeding up or slowing down, but in physics, acceleration is defined more generally as the rate of change of velocity. Because velocity has both magnitude and direction, acceleration can occur when either the speed changes, the direction changes, or both. This conceptual question checks whether you understand that subtlety.

Given Data / Assumptions:
- The body under consideration has a non zero acceleration.- Velocity is treated as a vector quantity with both magnitude (speed) and direction.- We neglect complications such as relativistic effects and focus on Newtonian mechanics.

Concept / Approach:
Acceleration is defined as the rate of change of velocity with respect to time. Since velocity is a vector, any change in its magnitude or its direction constitutes a change in velocity, and hence acceleration. For purely straight line motion with changing speed, both speed and velocity magnitude change. For uniform circular motion, however, the speed remains constant while direction continuously changes, and there is still acceleration toward the centre. Therefore, acceleration does not always require a change in speed, only a change in velocity, which may arise from direction change alone.

Step-by-Step Solution:
1. Recall the vector definition of velocity and that acceleration measures how quickly this vector changes.2. Recognise that change in velocity can be due to change in speed, change in direction, or both.3. Consider an example of straight line motion where the body speeds up or slows down; here both speed and velocity change.4. Consider uniform circular motion, where the speed remains constant but the direction of velocity continuously changes; acceleration is present even though speed is constant.5. From these examples, conclude that when a body is accelerated, its speed may change or may remain constant, but its velocity definitely changes.6. Therefore, the correct statement among the options is that its speed may or may not change.

Verification / Alternative check:
Mathematically, acceleration a can be written as a = dv / dt, where v is the velocity vector. In uniform circular motion, even though the magnitude of v is constant, the vector still rotates in direction, leading to a non zero derivative. Textbook examples always highlight that a stone tied to a string and whirled in a circle is undergoing centripetal acceleration without any change in speed. This reinforces the conclusion that speed change is not mandatory for acceleration to exist.

Why Other Options Are Wrong:
- Its velocity never changes: By definition, acceleration implies change in velocity, so this statement contradicts the very definition.- Its speed will always change: Speed can remain constant in cases like uniform circular motion while acceleration is still present.- Its direction always changes: In straight line motion with changing speed, the direction may remain the same while magnitude changes, yet there is acceleration.

Common Pitfalls:
Many students equate acceleration with speeding up and ignore the role of direction. This leads to confusion in topics such as circular motion, projectiles, and motion in two dimensions. A good strategy is to always remember that velocity is a vector and acceleration measures changes in that vector. If either component, magnitude or direction, changes, acceleration is present, and this may or may not coincide with a change in speed.

Final Answer:
When a body is accelerated, its speed may or may not change, but its velocity always changes.