Vectors - velocity is changing but speed is not

[kenji1992]

Vectors -- velocity is changing but speed is not...

Homework Statement

Which pair of vectors represent an object whose velocity is changing but whose speed is NOT changing?

Homework Equations

The Attempt at a Solution

E? V is going left, indicating negative, while acceleration goes in the other direction.

 

[NascentOxygen]

E? V is going left, indicating negative, while acceleration goes in the other direction.

But that acceleration is going to change the speed. It will, initially, decrease the speed. E is not correct.

 

[kenji1992]

#C, D, E can't be correct then by that logic... I hope I'm interpreting that correctly.

 

[haruspex]

#C, D, E can't be correct then by that logic... I hope I'm interpreting that correctly.

Right... and one more - which?

 

[HalfLostAndSearching]

This is an interesting question that highlights the difference between velocity and speed. Velocity is a vector quantity that includes both magnitude (speed) and direction, while speed is a scalar quantity that only considers the magnitude of an object's motion.

In order for an object's velocity to be changing, there must be a change in either its magnitude or direction. However, if the magnitude of an object's motion (i.e. its speed) is not changing, then its speed will remain constant while its direction may change. This means that the object's velocity is changing, but its speed is not.

To answer the question, the pair of vectors that represent an object with changing velocity but constant speed would be one where the direction of the velocity is changing, but the magnitude of the velocity remains the same. This could be represented by a circular motion, where the object's velocity is constantly changing direction but its speed remains constant.

In summary, velocity is a vector quantity that takes into account both the magnitude and direction of an object's motion, while speed is a scalar quantity that only considers the magnitude of an object's motion. An object's velocity can change without its speed changing if there is a change in direction but not magnitude of its motion.