An object in linear motion have a constant speed and changing velocity? Constant velocity and changing speed?

Question

My cousin recently took a test, and her answers seem correct to me but she was still marked off, can you guys help out?

A physics book is moving across a table. Can the book have a constant speed and a changing velocity? What about a constant velocity and a changing speed? Explain your answers.

Answer 1

Usually the word velocity is used to describe the vector and speed to the scalar.
So, if you're going around in circles at constant speed, your velocity is changing (the vector rotates).
But in linear motion it doesn't make sense (to me).

You can't have constant velocity and changing speed. If the velocity is constant that implies direction and magnitude (speed).

Answer 2

By definition, veloctiy is the vector change in displacement of an object divided by the change in time. Whereas speed is the scalar magnitude of that velocity. Thus,
1) Yes, the physics book can have a constant speed and a changing velocity. If the table is not level, the book could change directions (hence velocity) while still sliding at the same speed. Roll a ball across an uneven surface, and you will observe this happening.
2) No, the physics book cannot slide with constant velocity and changing speed. If the scalar magnitude of a vector changes, so does the vector. Changing speed necessarily changes velocity.

The space shuttle example cited above provides an incorrect conclusion. When displacement is occurring in three dimensions, velocity is also measured in three dimensions.
Although the space shuttle might have a "vertical velocity," this is only one component of the space shuttles velocity. It is not correct to say that one component alone of velocity can define velocity. Otherwise, velocity would be manipulated by the choice of reference frames and become meaningless. For example, if you choose horizontal movement in the North-South direction as your choice of component, you could equally conclude that the space shuttle had 0 velocity because it had no displacement along that axis. Of course, that conclusion would be wrong because ALL of the components together define the vector.

Answer 3

Changing Velocity

Answer 4

Velocity Synonyms

Answer 5

Yes. Velocity is a vector and speed is the magnitude of the velocity vector. So you can have a changing velocity vector with a constant magnitude. Consider your car moving in a circle but you keep the speedometer right at 35 mph. Your speed is 35 mph and is a constant but your direction is always changing so your velocity changes...

On the contrary, if you have a constant velocity that means that both the magnitude and direction do not change, so the speed cannot change either.

Answer 6

Speed is just a raw number, but velocity depends on the direction of motion. If the book is moving in a curve and speeding up, its velocity in the original direction could remain the same. Suppose it starts out moving north, but curves toward the east. As it does this, part of its motion is north, and part east. If it speeds up, the northward motion could conceivably remain constant. So that's the second scenario you mentioned. If the book goes in a curve but stays at the same speed (like a car going around a curve), the velocity in the original direction will decrease as the velocity in the new direction increases. That's the first scenario you mentioned. So, both situations are possible.

Actually, the second scenario is what happens when the Space Shuttle lifts off. It starts out vertically, but gradually curves toward the horizontal as it approaches orbit. It's going faster and faster (the speed), but it's vertical velocity could be about the same throughout part of the flight.

Answer 7

Aren't speed and velocity synonyms?