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.

Answer 1

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.