# Is my textbook wrong (acceleration problem)

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)) / $$\Delta$$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)

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.
You don't know where the object is on the x axis, you only know its velocity.

The acceleration is positive as you say, so at time 0, when the object was moving in the negative direction, the object was slowing down. At time 1 when the object was moving in the positive direction the object was speeding up.

In other words, the object, originally moving in the negative direction, slowed down, came to a stop, and then sped up in the positive direction.

HallsofIvy
Homework Helper
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.
Do you mean positive acceleration?
Initially the object was going to the left (x decreasing, negative velocity) finally, it was going to the right (x increasing, positive velocity)

[quoote]Ok, so what about the acceleration?

I have ax= lim ((5 - (-10)) / $$\Delta$$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)[/QUOTE]
You statement that velocity is positive is wrong. The velocity is negative for part of the motion, positive for part.

Ok, thanks guys it all makes sense to me now that I read and understood your postings. I appreciate it!