The work done by a body on the application of a constant force is the product of the constant force and the distance travelled by the body in the direction of the force. Express this in the form of a linear equation in two variable (work w and distance d), 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 it on the graph.
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Answer
1
Express the work done w in terms of the force F and distance d.
$w = F × d$
2
Substitute the constant force F = 3 to obtain a linear equation in w and d.
\text{$w = {color:#2E2EFF}3{/color} × d = 3d$}
3
Choose a few values of d and calculate the corresponding values of w to plot the line.
The table shows some sample values of $d$ and $w$.
$d$
$w$
0
0
1
3
2
6
4
Plot the points and join them to draw the straight line.
Answer: Graph of the equation w = 3d
5
Calculate the work done when the distance travelled is 2 units.
\text{$w = 3 × {color:#2E2EFF}2{/color}$}
$w = 6$
6
Verify the result using the graph.
Answer: In the graph in Step 4, the point $(2, 6)$ lies on the line $w = 3d$. Hence, when $d = 2$, the work done is $w = 6$ units.
