- #1
nissan4l0
- 11
- 0
My textbook, University Physics 12th ed, claims that the sign of x-acceleration does not tell you whether a body is speeding up or slowing down. It claims that the body is speeding up only when the velocity and acceleration have the same sign. Likewise, it claims that a body is slowing down only when the velocity and acceleration differ in signs.
I tried to prove this to myself and found an inconsistency.
v0x = -10 m/s
v1x = 5 m/s
Here, the magnitude of the velocity (speed) is decreasing. The velocity vector itself is positive, since it is going from the negative x-axis to the positive x axis.
So we have a decreasing speed and a positive velocity.
Ok, so what about the acceleration?
I have ax= lim ((5 - (-10)) / [tex]\Delta[/tex]t which is a positive quantity.
So we have a positive acceleration.
According to my book a positive sign on the velocity and a positive sign on the acceleration produce an increase in speed. Am I analyzing this in the wrong manner?(sorry for the poor formatting, I'll improve with time)
I tried to prove this to myself and found an inconsistency.
v0x = -10 m/s
v1x = 5 m/s
Here, the magnitude of the velocity (speed) is decreasing. The velocity vector itself is positive, since it is going from the negative x-axis to the positive x axis.
So we have a decreasing speed and a positive velocity.
Ok, so what about the acceleration?
I have ax= lim ((5 - (-10)) / [tex]\Delta[/tex]t which is a positive quantity.
So we have a positive acceleration.
According to my book a positive sign on the velocity and a positive sign on the acceleration produce an increase in speed. Am I analyzing this in the wrong manner?(sorry for the poor formatting, I'll improve with time)