Below are four pairs of velocities:
1) -35m/s 35m/s
2) -35m/s -45m/s
3) 35m/s east 35m/s north
4) 35m/s west 35m/s west

Which of the four pairs has the same speed and same velocity? Which of the four pairs has the same speed and different velocities? Which of the four pairs have different speeds and different velocities? Explain how you know.

Question

Below are four pairs of velocities:
1) -35m/s            35m/s
2) -35m/s            -45m/s
3) 35m/s east      35m/s north
4) 35m/s west      35m/s west

Which of the four pairs has the same speed and same velocity? Which of the four pairs has the same speed and different velocities?  Which of the four pairs have different speeds and different velocities? Explain how you know.

kainui · Answer

Remember, velocity is a vector and speed is a scalar quantity. What does that mean? A vector is a magnitude and direction while a scalar is just a magnitude. What's a magnitude and direction? Well hopefully you know what a direction is, left, right, up down, forwards, backwards, etc... while a magnitude is just an amount or number, like 155, 13, 33, 77 whatever, simple numbers.

One way of noting direction is by saying if something is negative or positive. For instance, if something is going down, you might like to refer to that as being direction in the negative y-axis. Or, you can use negative to mean left or positive to mean right. You can choose whichever is most appropriate to the situation, maybe going to the left makes more sense as a positive value.

So quick recap. Vectors have magnitude and direction, direction can be defined by negative/positive, east/west, forwards/backwards. Scalars are simply a magnitude without a direction.

65 mph to the east is a vector
65 mph is a scalar since it could be in any direction, it doesn't say

anonymous · Answer

So same speed and same velocity would be like pair 1? and same speed and different velocity would be like 3 and 4? and different speeds and different velocities would be pair 2?

kainui · Answer

The first pair has the same speed, but not the same velocity since the magnitudes are the same only; you can tell that they have different velocities because one is negative and the other is positive.

The third pair has the same speed and different velocity, exactly, but the fourth one has the same magnitude (35 m/s) and same direction (west) so they have the same speed and velocity.

For number two, you're correct, they're completely different, even though they have the same direction, it's the different magnitudes that prevent them from being the same speed or velocity.

Hope that helps clear things up for you. =D