Question

a cyclist traveled km moving at a constant speed. write down a formula that show's the dependence of the speed, v, on the time, t. find v(5), v(7), v(3.5).

Answer 1

To establish a formula that shows the dependence of speed \( v \) on time \( t \), we can use the relationship between distance, speed, and time. The formula can be expressed as:

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

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

If the cyclist travels a distance \( d \), we can then express the speed as:

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

To find specific values for \( v(t) \), we need to know the distance \( d \). Let's assume the cyclist traveled a distance of \( d = k \) km. Then the formula for speed becomes:

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

Now, we can calculate \( v(5) \), \( v(7) \), and \( v(3.5) \) based on this formula.

1. For \( t = 5 \):

\[
v(5) = \frac{k}{5}
\]

2. For \( t = 7 \):

\[
v(7) = \frac{k}{7}
\]

3. For \( t = 3.5 \):

\[
v(3.5) = \frac{k}{3.5}
\]

To compute these values, we will need a specific distance \( k \). If you can provide the value of \( k \) (the distance traveled in km), we can calculate the exact speeds.