The velocity vector V1 has a magnitude of 3.0 m/s and is directed along the +x-axis. The velocity vector V2 has a magnitude of 2.0 m/s. The sum of the two is V3, so that V3 = V1+V2

true or false for each question

The magnitude of V3 can be -3.0 m/s
The x-component of V3 can be 2.0 m/s
The magnitude of V3 can be 0.0
The magnitude of V3 can be 5.0 m/s
The magnitude of V3 can be 6.0 m/s
The magnitude of V3 can be 1.0 m/s

The magnitude of V3 can be 5.0 m/s

To answer these true or false questions, we need to understand vector addition.

When adding vectors, both their magnitudes and directions are taken into account. In this case, V1 has a magnitude of 3.0 m/s and is directed along the positive x-axis. V2 has a magnitude of 2.0 m/s, but its direction is not given.

Now let's consider each statement:

1. The magnitude of V3 can be -3.0 m/s. - False. Magnitudes are always positive values, so V3 cannot have a negative magnitude.

2. The x-component of V3 can be 2.0 m/s. - False. The x-component of V3 is the sum of the x-components of V1 and V2. Since V1 is directed along the positive x-axis and V2's direction is not given, it is not possible for the x-component of V3 to be 2.0 m/s.

3. The magnitude of V3 can be 0.0. - True. If V1 and V2 have opposite magnitudes and are directed along the same line but in opposite directions, their sum will have a magnitude of zero.

4. The magnitude of V3 can be 5.0 m/s. - True. If the magnitudes of V1 and V2 add up to 5.0 m/s and their directions are aligned, then the magnitude of V3 can indeed be 5.0 m/s.

5. The magnitude of V3 can be 6.0 m/s. - False. Since the magnitude of V1 is 3.0 m/s and the magnitude of V2 is 2.0 m/s, the maximum possible magnitude of V3 is 5.0 m/s.

6. The magnitude of V3 can be 1.0 m/s. - False. The magnitudes of V1 and V2 are already larger than 1.0 m/s, so the magnitude of V3 cannot be smaller than either of them.

Therefore, the correct answers are:

False
False
True
True
False
False