Is it possible for an object moving with a constant speed to accelerate?

Question

BlackTom AI · Accepted Answer

Acceleration is the rate of change of velocity. Velocity is a vector (has magnitude and direction), while speed is only the magnitude. Therefore velocity can change if either the magnitude (speed) changes or the direction changes.

1) Relevant concepts
- Velocity v is a vector; speed = |v|.
- Acceleration a = dv/dt, the time derivative of the velocity vector.
- A nonzero dv/dt (change in direction or magnitude) means nonzero acceleration.
- Example physical case: uniform circular motion — speed constant, direction changes continuously, producing centripetal acceleration a = v^2/r toward the center.

2) Step-by-step reasoning
- If speed is constant but direction changes, the velocity vector changes because its orientation changes.
- Since acceleration is the rate of change of velocity, any change in direction implies acceleration ≠ 0.
- Therefore constant speed does not guarantee zero acceleration.

3) Calculation example (intermediate steps)
- Consider motion in a circle of radius r with constant speed v.
- The centripetal acceleration magnitude is a = v^2 / r.
- For v = 10 m/s and r = 5 m: a = (10 m/s)^2 / (5 m) = 100 / 5 = 20 m/s^2.
- This shows a concrete nonzero acceleration while speed (10 m/s) stays constant.

4) Why the correct answer is correct
- The statement "Yes, although the speed is constant, the direction of the velocity can be changing" matches the vector definition of velocity and the derivative a = dv/dt. Changing direction changes v, so acceleration can be present even with constant speed.

5) Why the other options are incorrect
- "No, if the speed is constant then the acceleration is equal to zero." Incorrect because it ignores directional changes of velocity.
- "No, an object can accelerate only if there is a net force acting on it." Misleading: Newton’s second law says net force causes acceleration, but net forces can change direction without changing speed (e.g., centripetal force), so acceleration can occur with constant speed.
- "Yes, if an object is moving it can experience acceleration." Too vague/wrong implication: an object can move without accelerating (constant velocity).

6) Conclusion
Therefore the correct answer is: "Yes, although the speed is constant, the direction of the velocity can be changing." This matches the provided correct answer.

Is it possible for an object moving with a constant speed to accelerate?Single choice

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