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 by taking the constant force as 5 units. Find the solution graphically.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body.

Let assume that

• Work done is represented as y

• Distance travelled is represented as x.

Given that Constant force is 5 units

So,

$\bf\implies \:y = 5x$

➢ Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y = 5 \times 0$

$\rm\implies \:y = 0$

➢ Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:y = 5 \times 1$

$\rm\implies \:y = 5$

➢ Substituting 'x = 2' in the given equation, we get

$\rm :\longmapsto\:y = 5 \times 2$

$\rm\implies \:y = 10$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 1 & \sf 5 \\ \\ \sf 2 & \sf 10 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 0), (1 , 5) & (2 , 10)

➢ See the attachment graph.

Answer 2

Let x units be the distance traveled by the body and y units be the work done by constant force.

According to problem, y=5x     ...(1)

Now , putting the value x=0 in (1)

y=5×0=0

So, the solution is (0,0)

Putting the value x=1 in (1)

y=5×1=5

So, the solution is (1,5)

Putting the value x=2 in (1)

y=5×2=10

So, the solution is (2,10)

(i) When x=2 units (distance)

Putting the value x in (1)

y=5x

y=5×2=10.

Hence, Work done =10.

(ii) When x=0 units (distance)

Putting the value x in (1)

y=5x

y=5×0=0.

Hence, work done =0.