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 by taking the constant mass equal to 8kg. Find the force required, when the acceleration produced is $6 ms − 2$ .

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F = 6 a

, 30N

F = 5 a

, 40N

F = 8 a

, 48N

F = 5 a

, 25N

answer is C.

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Detailed Solution

Given force is directly proportional to the acceleration and constant mass = 8kg.
Let the force be F and acceleration be a.

⇒ F ∝ a ⇒ F = m a, where m is the mass constant .

⇒ F = 8 (a) ⇒ F = 8 a

Substitute

a = 6 m s − 2

in the derived linear equation.

⇒ F = 8 (6) ⇒ F = 48 N

Therefore,

F = 8 a

is the required linear equation and for

a = 6 m s − 2

,F = 48N.
Hence, option (3) is correct.

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