Q12P - Fundamentals Of Physics

Question

Question: The fastest growing plant on record is a Hesperoyucca whipplei that grew 3.7 m in 14 days. What was its growth rate in micrometers per second?

Step-by-Step Solution

Answer

Answer

 

The growth rate of plants in micrometers per second is$3.1\mu m/s$ .

Step 1: Given data

The height by which the plant grew, h=3.7 m

The time taken by the plant to grow, t = 14 days

 

Step 2: Understanding the growth rate

The growth rate is the rate of change in height of the plant and is a function of time. To find the rate of growth the height of the plant is to be measured with respect to time. 

 

The expression for the growth rate is given as follows: 

     $growth rate =\frac{h}{t}$                                   … (i)

 

Here,h  is the growth in height and t is the time.

Step 3: Conversion of the height and time in required units.

Convert the growth of the plant (h) into micrometers and days (t) in seconds.

$$\begin{gathered} h= 3.7m\times \frac{{10}^6\mu m}{m} \\ =3.7\times {10}^6\mu m \\ t = 14 days\times \left(\frac{24 hour}{day}\right)\times \left(\frac{60min}{hr}\right)\times \left(\frac{60s}{min}\right) \\ = 1,250.600s \end{gathered}$$

Thus, $3.7\times {10}^6$the height is and timespan is 1,250,600s.

Step 4: Determination of the growth rate.

Using equation (i), the growth rate of plant is calculated as: 

$$\begin{gathered} growth rate =\frac{h}{t} \\ =\frac{3.7\times {10}^6\mu m}{1209600s} \\ =3.1\mu m/s \end{gathered}$$

 

Thus, the growth rate of plants is$3.1\mu m/s$

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