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The work done by a body on application of a constant force is the product of the constant force and the distance travelled by the body in the direction of force. Express this in the form of a linear equation in two variables and draw its graph by taking the constant force as $3$ units. What is the work done when the distance travelled is $2$ units. Verify it by plotting the graph.
Solution
Work done $=($ constant force $) \times($ distance $)$
$=3 \times($ distance $)$
i.e., $y=3 x$, where $y$ (units) is the work done and $x$ (units) is the distance travelled. since $x=2$ units (given), therefore, work done $=6$ units. To plot the graph of the linear equation $y=3 x,$ we need at least two solutions of the equation. We see that $x=0, y=0$ satisfies the given equation also $x=1$ $y=3$ satisfies the equation.
Now we plot the points $A (0,0)$ and $B (1,3)$ and join $AB$ (see $Fig.$). The graph of the equation is a straight line. [We have not shown the whole line because work done cannot be negative].
To verify from the graph, draw a perpendicular to the $x$ -axis at the point $(2,0)$ meeting the graph at the point $C.$ Clearly the coordinates of $C$ are $( 2,6 ).$ It means that the work done is $6$ units.
