Question

All of the following are equivalent except _____.

dt = r
d = rt
d/t = t
d/t = r

Answer 1

To analyze the statements and determine which one is not equivalent, let's recall some basic relationships from the distance formula in physics:

1. **Distance** \(d\) is given by the formula:
\[
d = rt
\]
where \(r\) is the rate (speed) and \(t\) is the time.

2. From the relationship \(d = rt\), we can derive:
- \(r = \frac{d}{t}\)
- \(t = \frac{d}{r}\)

Now, let's evaluate each statement:

1. **\(dt = r\)**:
- This is not a standard relationship in physics. It seems to suggest multiplying distance by time gives a rate, which is not correct.

2. **\(d = rt\)**:
- This is indeed the formula for distance.

3. **\(\frac{d}{t} = r\)**:
- This is a correct derivation from the distance formula.

4. **\(\frac{d}{t} = t\)**:
- This simplifies to \(d = t^2\), which does not follow from the standard distance-speed-time relationships.

Thus, the statement that is not equivalent to the others is:

**\(dt = r\)**.