a cyclist traveled 70 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 express the dependence of speed $v$ on time $t$ for the cyclist who traveled a distance of 70 km at a constant speed, we start with the formula:

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$$

Let $d=70$ km (the distance traveled) and $t$ be the time in hours. Then, the formula for speed $v$ as a function of time $t$ is:

$$v(t)=\frac{d}{t}=\frac{70}{t}$$

Now, we can find the values for $v(5)$, $v(7)$, and $v(3.5)$.

1. For $t=5$: $$v(5)=\frac{70}{5}=14\text{ km/h}$$

2. For $t=7$: $$v(7)=\frac{70}{7}=10\text{ km/h}$$

3. For $t=3.5$: $$v(3.5)=\frac{70}{3.5}=20\text{ km/h}$$

Thus, the speeds corresponding to the given times are:

• $v(5)=14$ km/h
• $v(7)=10$ km/h
• $v(3.5)=20$ km/h