Question

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.

Answer 1

Hint: Work is defined as force applied on a body multiplied by distance covered by it. We will draw the graph using the relation given in the question. The formula for Work done is e W=F*D ,where W is the work done , F is the force applied on the body and D is the displacement or distance travelled by the body after the Application of the force.

Complete step-by-step answer:
Now, we are given that work is directly proportional to distance travelled. So, we can write it as,
W $\alpha $ distance. Let the distance be x. So, by the definition of work, we have
W = 5x, where 5 is the force given in the question.
Now, to plot a graph we will take distance (x) on x-axis and work (y) on y-axis.
Now, for x = 0, w = 5(0) = 0,
for x = 1, w = 5(1) = 5,
for x =2, w = 5(2) = 10
Taking these values, we will draw a graph.

In the graph, work is at y-axis and distance is at x-axis. So, from the graph, we can see that,
At distance x = 2, y = 5(2) = 10 units.
At distance x = 0, y = 5(0) = 0 units.

Note: Whenever we come up with such types of questions, we will first make a relation using the condition given in the question. We will then put some values in the relation to plot the graph. Then with the help of these values, we will plot the graph. Like in this question, we make a relation according to the question. Then we will put some values in the relation and plot the graph from the values we get. After it, we will find the values asked in the question. Remember the force applied is considered for a specific value and hence is constant in this case.