Question

Suppose that a box is accelerating at a rate of $2m{s}^{-2}$. If the net force is tripled and the mass is doubled, then what is the new acceleration of the box?

• A. $6m{s}^{-2}$
• B. $4m{s}^{-2}$
• C. $3m{s}^{-2}$
• D. $2m{s}^{-2}$

Answer 1

The correct option is C $3m{s}^{-2}$

Let the initial acceleration be a, mass of the box be m, and the net force be $F$.
Given a = $2m{s}^{-2}$
According to Newton's Second Law of Motion,
$F$ = $m\times a$
$\Rightarrow$$F$ = $m\times 2$
$\Rightarrow$$\frac{F}{m}=2$ $\to$ eq(1)
Since the force F is tripled, the force becomes 3F and the mass is doubled, therefore the mass becomes 2m.
Let the new accelaration be a'.
$\Rightarrow$ a' =$\frac{3F}{2m}$
Substituting for $\frac{F}{m}$ from equation (1),
a' =$\frac{3}{2}$ $\times 2$
$\Rightarrow$ a' = $3m{s}^{-2}$