Question

An object has an acceleration of 12.0 m/s/s. If the net force was doubled and the mass were tripled, then the new acceleration would be _____ m/s/s.

Answer 1

Given :

✴ Case - I

⟶ Force = F

⟶ Mass = m

⟶ Acceleration = 12m/s²

✴ Case - II

⟶ Force = 2F

⟶ Mass = 3m

To Find :

➳ Acceleration in second case.

Concept :

⇒ This question is completely based on the concept of newton's second law of motion.

⇒ As per this law, Force is defined as the product of mass and acceleration.

Mathematically, F = ma

Calculation :

$\implies\sf\:\dfrac{F_1}{F_2}=\dfrac{m_1\times a_1}{m_2\times a_2}\\ \\ \implies\sf\:\dfrac{F}{2F}=\dfrac{m\times 12}{3m\times a_2}\\ \\ \implies\sf\:\dfrac{1}{2}=\dfrac{4}{a_2}\\ \\ \implies\sf\:a_2=4\times 2\\ \\ \implies\underline{\boxed{\bf{a_2=8\:ms^{-2}}}}$

Answer 2

New acceleration would be 12 m/s²

Given that;

Acceleration of object = 12 m/s²

New net force = 2f

New mass = 3m

Find:

New acceleration

Computation:

$\frac{F1}{F2} = \frac{m1a1}{m2a2} \\\\\frac{f}{2f} = \frac{m(12)}{(3m)a2} \\\\\frac{1}{2} = \frac{4}{a2} \\\\a2 = 8 m/s^2$

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