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

Let, the work done = y and let the distance = x
Given: the constant force = 5 units
Work done by the body is directly proportional to is distance travelled. Therefore, y α x
⇒ y = kx
Here, k is proportionality constant and givenk = 5 units.
Hence, y = 5x
For the graph:
Putting x = 0, we have, y = 5 × 0 = 0
Putting x = 1, we have, y = 5 × 1 = 5
Putting x = 2, we have, y = 5 × 2 = 10
Hence, A(0, 0), B(1, 5) and C(2, 10) are the three solutions of the
given equation.
(i) If the distance travelled is 2 units, the work done is 10 units.
(ii) If the distance travelled is 0 units, the work done is 0 units.