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 ms ^(-2) " " (ii) 6 ms^(-2)`

Explanation

Given that, the force (F) is directly proportional to the acceleration


(a). i.e., F ∝ a F∝a ⇒ F = m a ⇒F=ma [where, ,m=arbitrary constant and take value 6 kg of mass ] ∴ F = 6 a ∴ F=6a

(i) If `a = 5 m//s ^2`
`a=5m//s^2`, then from Eq.

(i), we get F = 6 × 5 = 30
`" F"=6×5=30N`

(ii) If `a = 6 m // s ^2 `
`a=6m//s^2`, then from Eq. (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.