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The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of 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 m/sec² , (ii) 6 m/sec²

Solution:

Given, the force exerted to pull a cart is directly proportional to the acceleration produced in the body.

We have to write a linear equation and draw the graph of the equation by taking the constant mass equal to 6 kg.

We have to read from the graph the force required when the acceleration produced is 5 m/sec²

Given, F ∝ a

So, F = ma

Where m is the arbitrary constant i.e.,constant mass

Given, m = 6 kg

Now, F = 6a

(i) The force required when acceleration is 5 m/sec² is

F = 6(5)

F = 30 N

Therefore, the force is 30 N

(i) The force required when acceleration is 6 m/sec² is

F = 6(6)

F = 36 N

Therefore, the force is 36 N

The points are (5, 30) and (6, 36)

On plotting the points on the graph and joining them

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of 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 m/sec² , (ii) 6 m/sec²

We obtain a straight line which is the graph of the equation F = 6a.

✦ Try This: 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 and draw the graph of the same by taking the constant force as 5 units. Also, read from the graph the work done when the distance travelled by the body is: (i) 2 units, (ii) 0 unit

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4

NCERT Exemplar Class 9 Maths Exercise 4.4 Problem 6

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of 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 m/sec² , (ii) 6 m/sec²

Summary:

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. The linear equation of two variables is F = 6a by taking the constant mass equal to 6 kg. The graph of the linear equation is mentioned above. The force required when the acceleration produced is (i) 5 m/sec² is 30 N, (ii) 6 m/sec² is 36 N

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