# Speed, Acceleration, Velocity

Tags:
1. Nov 26, 2015

### SydneyQuynn

1. The problem statement, all variables and given/known data
True or False question:
If speed is decreasing and acceleration is positive, then velocity must be decreasing.

I answered "true" on a test and chose incorrectly.

2. Relevant equations
When is acceleration positive when speed is decreasing?
Why most velocity be increasing?

2. Nov 26, 2015

### Ray Vickson

Velocity or acceleration (along a line) can be positive or negative; say positive = east and negative = west. Speed is always non-negative:
Speed = |Velocity|

So, if acceleration > 0 and speed is decreasing, velocity must be < 0; in other words, acceleration points east, but velocity points west. It is like you are driving west but putting on the brakes to slow down. Note that velocity is increasing (becoming less negative) even though speed is decreasing.

If it sounds confusing, just remember: while we may use the words "speed" and "velocity" almost interchangeably in casual conversation, in math and physics they are different and must be distinguished.

3. Nov 26, 2015

### I like Serena

I agree with you!
The question is a bit confusing, mixing speed and velocity, but if speed is decreasing, whatever the acceleration is, speed and velocity will still be decreasing.

4. Nov 26, 2015

### vela

Staff Emeritus
That's an incredibly bad test question. The phrase "velocity is decreasing" is ambiguous. A reasonable interpretation of the phrase is "the magnitude of the velocity, i.e., the speed, is decreasing." I'd guess there are a number of people who missed that question despite having a good understanding of the physics.