# Why Does 0 Velocity and Negative Acceleration = Increasing Speed?

## Homework Statement

Why Does 0 Velocity and Negative Acceleration = Increasing Speed?

None

## The Attempt at a Solution

I am using Halliday and Resnick (5th Edition), and the anwer key in the back says that speed is increasing at the point when velocity is zero, and acceleration is negative.

I am assuming I am wrong and the book is right. I just can't understand it though. If the rate of change of the position function is not changing, and the acceleration is decreasing, then doesn't that mean that the particle is going in a straight line and is slowing down?

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Speed is a scalar quantity so it doesn't matter whether you are going forwards or backwards. If you slow down you have negative acceleration; if you keep that negative acceleration after you stop, you then start to go backwards.
At the point you came to rest, you still had negative acceleration, zero velocity and zero speed. You then gained some negative velocity but your speed increased. (It's just a number)

Pengwuino
Gold Member
You have to be careful of the terminology. A "decreasing acceleration" mean a decreasing in magnitude acceleration while a "negative acceleration" simply means an acceleration in the negative direction. As for your problem, imagine a ball fired straight upwards in a gravitational field. It is always undergoing a constant negative acceleration. At the peak, however, the velocity and thus, speed, reaches 0. Now, at this point, the velocity is going to become negative but the speed, which is simply the magnitude, is going to increase.

"negative acceleration" simply means an acceleration in the negative direction.
That's what I've been needing to begin to cement this concept! Thank you for your very precise use of language.

arildno
Homework Helper
Gold Member
Dearly Missed
Hi. Love_to_Learn!

You will find out that the word "acceleration" is used in two rather different ways:

1. The acceleration/deceleration-concept couple:
This is the informal, colloquial way of saying the speed increases (acceleration), or the speed decreases (deceleration).

This is NOT "directionally specific", since "speed" is a quantity without direction

Note that the word "deceleration" is ONLY used in this context

2. Direction-specific acceleration:
Here, some direction is implied (say, for example, left vs. right, up vs down, or radially outwards vs radially inwards)

One of the anti-parallell directions is thought of as "positive", the other as "negative", giving rise to "positive acceleration" vs. "negative acceleration"

An often-met case is the couple centrifugal acceleration vs centripetal acceleration, where in "centrifugal acceleration" the positive direction is radially outwards, whereas the opposite is true for "centripetal acceleration".