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The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \,kg .$ Read from the graph, the force required when the acceleration produced is $(i)$ $5\, m / sec ^{2}$, $(ii)$ $6 \,m / sec ^{2}$
Solution
We have $y \propto x \Rightarrow y=m x$
Where $y$ denotes the force, $x$ denotes the acceleration and $m$ denotes the constant mass. Taking $m =6 \,kg$, we get $y =6 \,x$
Now, we form a table as follows by writing the value of $y$ below the corresponding value of $x$.
$\begin{array}{|l|l|l|l|} \hline X & 0 & 1 & 2 \\ \hline y & 0 & 6 & 12 \\ \hline \end{array}$
Plot the points $(0,0),(1,6)$ and $(2,12)$ on a graph paper and join any two points and obtain a line.
