# Solve this question .

Solution)

ββββLet 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.

Regards!

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