Question

Alexa's hair grows with an average speed of 3.5 × 10–9 m/s. how long does it take her hair to grow 0.30 m? note: 1 yr = 3.156 × 107 s.

Answer 1

we are given

speed  of 3.5 × 10^–9 m/s

Let's assume speed of hair is v

so,

$v=3.5*10^{-9}m/s$

now, we are given

her hair to grow 0.30 m

so,

$d=0.30m$

we have to find time (t)

so, we can use formula

$t=\frac{d}{v}$

we can plug values

and we get

$t=\frac{0.30}{3.5*10^{-9}}$

now, we can simplify it

$t=85714285.71429 s$

now, we know that

$1 yr = 3.156* 10^7 s$

we can find for 1s

$1s=\frac{1}{3.156* 10^7} yr$

$t=85714285.71429*1 s$

we can replace 1s

we get

$t=85714285.71429*\frac{1}{3.156* 10^7} yr$

now, we can simplify it

and we get

$t=2.71592 yrs$..............Answer

Answer 2

You can use the definition of average speed which is ratio of total distance(length) covered(incremented) to total time taken to do so.

The time it will take her hair to grow 0.30 meters is 2.714 years approximately

How is average speed calculated?

The average speed is the ratio of total length traveled(or incremented here, its actually measure of change in spatial distance) to total time taken to travel that length.

Thus, if

$d_2 = \text{final position}\\d_1 = \text{initial position}\\t_2 = \text{end time}\\t_1 = \text{start time}$

then,

$S_a = \dfrac{\varDelta d}{\varDelta t} = \dfrac{d_2 - d_1}{t_2 - t_1}$

where is average speed denoting average rate of change of distance(here length) as per unit time.

Since her average hair growth speed was $S_a = 3.5 \times 10^{-9} \: \rm m/s$

and the difference in length is needed to be $\varDelta d = 0.30 \: \rm m$

Thus, the difference in time (the time needed) will be calculated as

$S_a = \dfrac{\varDelta d}{\varDelta t} \\\\3.5 \times 10^{-9} = \dfrac{0.30}{\varDelta t}\\\\\varDelta t = \dfrac{0.30}{3.5 \times 10^{-9}} \: \rm seconds\\\\\varDelta t = \dfrac{0.30}{3.5} \times 10^9 \: seconds = 0.0857 \times 10^9 \: seconds = 8.57 \times 10^{9-2} \: sec.\\\\ (since \: a^{-b} = \dfrac{1}{a^b} , or \: a^b = \dfrac{1}{a^{-b}})\\\\\varDelta t = 8.57 \times 10^7 \: seconds$

Since it is known that $1 \: \rm year = 3.156 \times 10^7 s$  , thus,

Converting the time needed for her hair to grow 0.30 meter from seconds to years, we get

$1 \: \rm year = 3.156 \times 10^7 s\\1 \: s = \dfrac{1}{3.156 \times 10^7} \: year\\\\8.57 \times 10^7 \: s = \dfrac{8.57 \times 10^7}{3.158 \times 10^7} \: years = \dfrac{8.57}{3.158} \approx 2.714 \: years$

Thus,

The time it will take her hair to grow 0.30 meters is 2.714 years approximately

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