Question: The force exerted to pull a cart is directly proportional to the acceleration produced in the body Express the - Maths - Linear Equations in Two Variables

Question

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

Gopal Mohanty · Accepted Answer

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:
<img alt="" height="287" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/15Feb2011-1%20png"
width="286">
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
Cheers!