Question

The acceleration of an object is inversely proportional to _____________

Answer 1

Step 1. Theorem used

From Newton's $2^{nd}$ law of motion, we get, that the rate of change of momentum is directly proportional to the applied force on that object.

Step 2. Find the relation

Let $m$ be the mass and $v$ the velocity of the object.

Therefore the momentum is $mv$.

So the rate of change of momentum is $\frac{d\left(mv\right)}{dt}$ [differentiating with respect to time$\left(t\right)$ ]

If $F$ is the applied force then,

$$\begin{gathered} F=\frac{d\left(mv\right)}{dt} \\ \Rightarrow F=m\frac{dv}{dt} \\ \Rightarrow F=ma\left[\because \frac{dv}{dt}=a=\mathrm{acceleration}\right] \\ \Rightarrow \frac{F}{m}=a \end{gathered}$$

$\therefore a\propto F$ and $a\propto \frac{1}{m}$

Therefore, acceleration is inversely proportional to the mass of the object.

Hence, the answer is the mass of the object