Question

which represent correct variations of the formula for speed? check all that apply.
$t = \frac{d}{s}$
$s = \frac{d}{t}$
$t = \frac{s}{d}$
$s = dt$
$d = st$
$d = \frac{s}{t}$

Explanation:

The basic formula for speed is \( s=\frac{d}{t} \), where \( s \) is speed, \( d \) is distance, and \( t \) is time. We can derive other formulas by rearranging this equation.

Step 1: Analyze \( t = \frac{d}{s} \)

Starting from \( s=\frac{d}{t} \), multiply both sides by \( t \): \( st = d \). Then divide both sides by \( s \): \( t=\frac{d}{s} \). This is a correct rearrangement.

Step 2: Analyze \( s=\frac{d}{t} \)

This is the original formula for speed (speed equals distance divided by time), so it is correct.

Step 3: Analyze \( t=\frac{s}{d} \)

From \( st = d \) (derived from \( s=\frac{d}{t} \)), dividing both sides by \( d \) gives \( \frac{st}{d}=1 \), which is not equivalent to \( t=\frac{s}{d} \). So this is incorrect.

Step 4: Analyze \( s = dt \)

From \( s=\frac{d}{t} \), multiplying both sides by \( t \) gives \( st = d \), not \( s = dt \). So this is incorrect.

Step 5: Analyze \( d = st \)

Starting from \( s=\frac{d}{t} \), multiply both sides by \( t \): \( st = d \), or \( d = st \). This is a correct rearrangement (distance equals speed multiplied by time).

Step 6: Analyze \( d=\frac{s}{t} \)

From \( st = d \) (derived from \( s=\frac{d}{t} \)), dividing both sides by \( t \) gives \( s=\frac{d}{t} \), not \( d=\frac{s}{t} \). So this is incorrect.

Answer:

• \( t=\frac{d}{s} \) (correct)
• \( s=\frac{d}{t} \) (correct)
• \( d = st \) (correct)

So the correct options are:

• \( t=\frac{d}{s} \)
• \( s=\frac{d}{t} \)
• \( d = st \)