Question

During the summer, when your lawn is growing quickly, estimate this speed, in m/s. Make this estimate from your experience noting, for instance, how often you mow the lawn and what length you trim.

Answer 1

Answer: If T is the time you wait to trim the lawn since you last did it and B is the lenght at which you trim, then the speed will be:

$v=\frac{B}{T}$

Explanation:

Let's say T is the time you wait to trim the lawn since you last did it (1 month for example) and B is the lenght at which you trim (10cm for example).

If v is the speed at which the lawn grows, then the lenght of the lawn as a function of time will be:

$b(t)=b_{0}+ vt$

where $b_{0}$ is an arbitrary initial lenght. Let's say $b_{0}=0$.

$b(t)=vt$

Then we have:

$v=\frac{b(t)}{t}$

So, at time T the lawn has grown a lenght B. And the speed is:

$v=\frac{B}{T}$