In motion along a path, which of the following statements about an object moving with constant speed is correct?

Introduction / Context:
Students often confuse speed and velocity. Speed is a scalar that tells how fast an object moves, while velocity is a vector that includes both speed and direction. Acceleration is related to changes in velocity. This question probes whether you understand that an object may have constant speed but still experience acceleration if its direction of motion changes, such as in uniform circular motion.

Given Data / Assumptions:
- The object is stated to move with constant speed, meaning the magnitude of velocity is constant.
- No restriction is given on whether the direction of motion changes.
- Options discuss acceleration and velocity properties under constant speed conditions.

Concept / Approach:
Acceleration is defined as the rate of change of velocity, not just speed. If an object moves in a straight line at constant speed, its velocity vector does not change in either magnitude or direction, so acceleration is zero. However, if the object moves in a curved path or circle at constant speed, the direction of the velocity vector keeps changing, and the object has centripetal acceleration even though speed is constant. Therefore, the safest statement is that an object with constant speed might be accelerated depending on whether its direction changes.

Step-by-Step Solution:
Step 1: Recognise that constant speed does not automatically mean constant velocity, because direction may still change. Step 2: Recall that acceleration depends on change in velocity, which includes both magnitude and direction. Step 3: Consider motion in a straight line at constant speed: in this special case, velocity is constant and acceleration is zero. Step 4: Consider uniform circular motion at constant speed: here the direction changes continuously, so there is centripetal acceleration towards the centre. Step 5: Since both possibilities exist, the correct statement is that the object might be accelerated.

Verification / Alternative check:
Uniform circular motion is the classic example where speed is constant but acceleration exists. The magnitude of this centripetal acceleration is v^2 / r and points towards the centre of the circle. This clearly demonstrates that constant speed does not guarantee zero acceleration. On the other hand, a car cruising along a straight highway at unchanging speed has neither tangential nor centripetal acceleration, showing that zero acceleration is also possible. Combining these examples confirms that "might be accelerated" is the correct general statement.

Why Other Options Are Wrong:
Is not accelerated: This would only be true if the direction were also constant. In general, with possible curved paths, this is not always correct.
Is always accelerated: This overstates the case. Straight-line motion at constant speed has zero acceleration, so acceleration is not guaranteed.
Also has a constant velocity: Constant speed does not ensure constant velocity unless direction is fixed. In circular motion the velocity is changing direction, so it is not constant.

Common Pitfalls:
A common misunderstanding is thinking that any acceleration must involve changes in speed. Students may incorrectly assume that if a speedometer reading does not change, acceleration must be zero. To avoid this, remember that velocity is a vector and that changing direction at constant speed still changes the velocity, producing acceleration. Always check both magnitude and direction when reasoning about acceleration.

Final Answer:
An object moving with constant speed might be accelerated, depending on whether its direction of motion changes.