Question

A cyclist traveled 70 km moving a constant speed. Write down a formula that shows the dependence of speed, v, on time, t. Find v(5), v(7), v(3.5).

Answer 1

To express the relationship between speed, distance, and time, we can use the formula:

\[
v = \frac{d}{t}
\]

where:
- \( v \) is the speed,
- \( d \) is the distance traveled, and
- \( t \) is the time taken.

In this scenario, the cyclist traveled a distance \( d = 70 \) km. Therefore, we can rewrite the formula as:

\[
v = \frac{70}{t}
\]

Now, we can find the speed for different times.

1. For \( t = 5 \) hours:

\[
v(5) = \frac{70}{5} = 14 \, \text{km/h}
\]

2. For \( t = 7 \) hours:

\[
v(7) = \frac{70}{7} = 10 \, \text{km/h}
\]

3. For \( t = 3.5 \) hours:

\[
v(3.5) = \frac{70}{3.5} = 20 \, \text{km/h}
\]

Thus, the formula that shows the dependence of speed on time is:

\[
v(t) = \frac{70}{t}
\]

And the calculated speeds are:
- \( v(5) = 14 \, \text{km/h} \)
- \( v(7) = 10 \, \text{km/h} \)
- \( v(3.5) = 20 \, \text{km/h} \)