__Question: __The force exerted to pull a cart is directly proportional to the acceleration produced in the body.Express the statement as a linear equation in two variables and draw the graph of the same by taking the constant mass equal to 6 kg.Read from the graph the force required when the acceleration produced is :

(i) 5 cm/sec2 (ii) 6 cm/sec2

Here is the answer to your question.

Let the force exerted to pull the cart is denoted by

*y*and the acceleration is denoted as*x*Given that

*y*α*x*⇒

*y*=*kx*Given that the constant mass

*k*is equal to 6 kg∴

*y*= 6*x*Three solutions satisfying this equation are (0, 0), (1, 6), (2, 12)

The equation

*y*= 6*x*can be represented graphically as:To find the force required to produce the acceleration of 5 cm/s

^{2}, draw a line parallel to*y*-axis from (5, 0) . Let it intersects the graph at point P. from P draw a line parallel to*x*-axis to intersect*y*-axis. It may be observed that intersects*y*-axis at (0, 30). This is shown in the graph in red line.Thus, the force of 30 kg cm/s

^{2}is required to produce an acceleration of 5 cm/s^{2}You can similarly find the force required to produce an acceleration of 6 cm/s

^{2}. You find it as 36 kg cm/s^{2}. This is shown in the graph in green lines.

Hope! This will help you.

Cheers!

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