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?单项选择题

类似问题

A car travelling at 20 m s-1 slows down to 15 m s-1 in 5 seconds. The car's acceleration in units of m s-2 is

Referring to Figure 1.17 in Chapter 1 of the text (reproduced below), when the student is traveling between 300m-500m, which of the following statements are correct?

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 9.8 seconds, if it reached a maximum speed of 8.3 m s-1?

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 9.8 seconds, if it reached a maximum speed of 8.3 m s-1?

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the deceleration (in m s-2) of the helicopter between t2 = 7 seconds and t3 = 11.6 seconds, if it reached a maximum speed of 12.4 m s-1?

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 7.9 seconds, if it reached a maximum speed of 10.0 m s-1?

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 7.9 seconds, if it reached a maximum speed of 10.0 m s-1?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单