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

Answer:

s(t)=7t

Explanation:

We are  given that

Length of side of square initially=0 cm

Side of square increasing at the rate=$\frac{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

$\frac{ds}{dt}=7$

$ds=7dt$

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.