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:

• \( v(5) = 14 , \text{km/h} \)
• \( v(7) = 10 , \text{km/h} \)
• \( v(3.5) = 20 , \text{km/h} \)