Question

The length of the sides of a square are initially 0 cm and increase at a constant rate of 7 cm per second. Write a formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing.

Answer 1

s(t)=7t

Step-by-step explanation:

We are given that

Length of side of square initially=0 cm

Side of square increasing at the rate=
`(ds)/(dt)=`7 cm/s

We have to find the formula to express the side length of the square s(in cm) in terms of the number of seconds t.

According to question

`(ds)/(dt)=7`

`ds=7dt`

Taking integration on both sides then, we get

`\int ds=7\int dt`

`s=7t+C`

Substitute t=0 and s=0

`0=0+C`

`C=0`

Now, substitute the value of C then, we get

s(t)=7t

This is required formula that express the side length of the square s(in cm) in terms of the number of seconds t, since the square's side length began growing.