If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as

Explanation

Let W be the work done by a force on a body and let x be the distance travelled by the body. Then,
`W proptox`
`rArr` W= Fx, where F is the constant force applied on the body
`rArr W= 3x [ :' F= 3 "units (given)"].`
Thus, the required equation in two variables is W = 3x . ... (A)
Putting x=1 in (A), we get W = `( 3 xx1) = 3`.
Putting x=3 in (A) , we get W=`(3 xx3) = 9.`
Putting x= 4 in (A) , we get `W =(3 xx4) = 12.`
Putting x = 5 in ( A) , we get W = `( 3 xx5) = 15.`
Thus, we have the following table.
`{:(x,1,3,4,5),(W,3,9,12,15):}`
On a graph paper draw mutually perpendicular lines X' OX and YOY' as the x- axis respectively.
Along the x- axis, take 10 small divisions = 1 unit and along the y- axis , take 5 small divisions = 1 unit.
On this graph paper, plot the points `A(1,3), B(3,9),C(4,12) and D(5,15)`. Join AB, BC and CD to obtain the graph line ABCD, shown below.

Produce the graph line ABCD in both the directions.
(i) Clearly, the graph line passes through the point O(0,0).
`:. x=0 rArrW=0.`
Thus, when the body travels 0 distance , the work done is 0.
(ii) Take a point G on the x- axis such that x=2.
Draw `GH bot` x-axis, cutting ABCD at H(2,6).
`:. x=0 rArrW=0.`
Thus, when the body travels 2 units, the work done is 6 units.