# Investigative and mathematical skills in science EMA

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Investigative and mathematical skills in science EMA

Question 1

(a) We know that

y= 4πLxFor the first part of problem (i), we have to find the base units of y.

It is given that L has units of meters (m) and x has units of meters per second per second (m/s2). In order to find the value of y, the following expression can be simplified while neglecting the constants which is 4π.

We have

y= mms2=m2s2= msHence the unit of y is meters per second (m/s).

(ii) For the second part of the question, a straight line can only be obtained if the equation can be expressed in the form of

y = mx + c

where m is the slope of line and c is the y-intercept.

Rearranging the above equation, we have

y= 4πL x xHowever x not a linear is function and will surely give a curve. But, if the above equation is bounded for only positive squared values of x, the above function would be a straight line. However, the constant terms would be the slope of that straight line.

(iii) When we have a straight line, with the data of x and y. We have to find the slope which can be found by

Slope m= ∆y∆xConsidering the equation, the slope would be positive and once the slope is known, it can be compared with general line equation (shown above) to find the value of L. Mathematically;

m= 4πL Rearranging the equation will give,

L= m24πThe above equation will determine the value of constant, L.

(b) The graph is provided and t…

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