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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 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 that, the force (F) is directly proportional to the acceleration (a).
i.e., F ∞ a
⇒ F = ma ...[Where, m = arbitrary constant and take value 6 kg of mass]
∴ F = 6a ...(i)
(i) If a 5 m/s2, then from equation (i), we get
F = 6 × 5 = 30 N
(ii) If a 6 m/s2, then from equation (i), we get
F = 6 × 6 = 36 N
Here, we find two points A(5, 30) and B(6, 36).
So draw the graph by plotting the points and joining the line AB.
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