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 = 6x
Three solutions satisfying this equation are (0, 0), (1, 6), (2, 12)
The equation y = 6x can be represented graphically as:
To find the force required to produce the acceleration of 5 cm/s2, 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/s2 is required to produce an acceleration of 5 cm/s2
You can similarly find the force required to produce an acceleration of 6 cm/s2. You find it as 36 kg cm/s2. This is shown in the graph in green lines.
Hope! This will help you.