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 5 units. Also read from the graph the work done when the distance travelled by the body is:
(i) 2 units (ii) 0 unit
Solution:
It is given that work done by a body on application of a constant force is directly proportional to the distance travelled by the body.
So, we have
where W is the work done and S is the distance travelled by the body.
where k is the constant force. (1)
It is equation consisting of two variables W and S. k is just a constant here.
We will draw graph of this equation taking
units. Putting
in (1), we get
To draw graph of
, we will find 3 or 4 set of solutions.
Putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Similarly, putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Therefore, three different solutions for equation
are:
Now, we plot all these three points on the Cartesian plane. When we join these points, it makes a straight line.
(i) We can read from the graph that when
units, we have
units
(ii) Similarly, when
units, we have
units.
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