Which of the Following is false?

[spockjones20]

Homework Statement

Which of the following statements is false?

A.) The velocity of an object can change while maintaining a constant speed.
B.)The speed of an object can change without the direction of its velocity vector changing.
C.)An object that has a non-zero acceleration must have a changing velocity.
D.) An object that maintains a constant speed must have zero acceleration.

Homework Equations

Speed = |Velocity|

Acceleration = ΔV/Δt

The Attempt at a Solution

I tried to go through these one at a time and treat each one as a separate true or false question. Here is my thought process.

A.) The velocity of an object can change while maintaining a constant speed.
- I thought this would be true because velocity takes direction into account, whereas speed does not. Therefore, you could change direction without changing the magnitude of your velocity, which would maintain a constant speed but change the overall velocity.

B.) The speed of an object can change without the direction of its velocity vector changing.
- I also thought this was true, since you can accelerate or decelerate linearly, which would change the magnitude of the velocity (and therefore the speed) without changing the direction.

C.) An object that has a non-zero acceleration must have a changing velocity.
- I think this is true. Acceleration, by definition, is a change in velocity with respect to time. Therefore, if acceleration ≠ 0, it seems as if velocity would have to change somehow.

D.) An object that maintains a constant speed must have zero acceleration.
- This gave me the most trouble. I think it is false, but I do not know why it technically would be, I am mostly just using the process of elimination. One thing I was not sure of was whether or not changing the direction but not changing the magnitude of velocity could be considered "acceleration." If it is, then this could be false. Otherwise, I am not sure what else would apply here.

So in the end, I personally think D is the culprit. All I am looking for is any corrections to be made in my above reasoning (if I reasoned correctly could you confirm it, I think I understand most of it but I'm at that uncertain point in the learning process where confirmation is helpful) and then, if D is the correct answer, it would be very helpful to have a more formal reason as to why D is false. Thank you very much in advance, and let me know if I can clarify any of the above statements.

 

[phinds]

Think about the characteristics of a ball on the end of a string that is spun around your head at a constant RPM
to see why you are right

 

[spockjones20]

Circular motion actually makes that a whole lot clearer in my head. Since it is constantly accelerating towards the center right? But at the same time speed is constant.

 

[phinds]

Circular motion actually makes that a whole lot clearer in my head. Since it is constantly accelerating towards the center right? But at the same time speed is constant.

exactly

 

[Nickie]

Yes, you are correct in your reasoning. A and B are true statements because velocity takes into account direction and speed does not. C is also true because acceleration, by definition, is a change in velocity over time.

D is the false statement. While it may seem counterintuitive, an object can maintain a constant speed while still having non-zero acceleration. This is possible if the object is changing direction but maintaining a constant speed. In this case, the velocity vector is changing, even though the speed is not. This can be seen in circular motion, where the object is constantly changing direction but maintaining a constant speed.

To further explain, acceleration is the rate of change of velocity, not speed. So even if the speed remains constant, if the direction of the velocity vector changes, then there is still a change in velocity and therefore non-zero acceleration.

I hope this helps clarify any confusion. Keep up the good reasoning!