# What is the effect of the mass of object on its acceleration? On its velocity? [closed]

A short answer will do, thankyou!

• That depends on more details. This is too broad. Oct 3, 2020 at 18:16

If I understand your question, you are asking about applications of Newton's Second Law: $$F=ma$$.

In the case of acceleration, you have

$$a=\frac{F}{m} \qquad(1)$$

which shows a greater mass, $$m$$, results in a smaller acceleration, $$a$$, for a given constant force, $$F$$.

In the case of velocity, the expression is:

$$v=at$$

Using $$a$$ from (1) above, this can be written as:

$$v=\frac{F}{m}t$$

From this, one can see that a greater mass will require more time, $$t$$, to reach a given velocity, again assuming a constant force, $$F$$.

I hope this helps.

I am assuming one-directional motion for simplicity.

Suppose you apply a Force $$F$$ on objects with different masses.

Then using Newton's Second Law:

$$a=F/m$$ Meaning that if mass becomes greater, acceleration becomes smaller.

Further $$a=dv/dt$$. Therefore $$dv = a dt = \frac Fmdt$$ $$\int{dv}=\Delta v= \int\frac Fm dt$$

Clearly for the same force F, for greater mass, change in velocity is smaller.

In case of free fall, Force on body is $$mg$$ , i.e., different for different masses. Here acceleration for any mass is then $$a=mg/m=g$$

This does not depend on mass as different amount of forces are acting on the body during free fall.

Short answer : Depends on the magnitude of force acting since two bodies of different mass can have same acceleration and thus same velocity after sometime if both were initially at rest or moving with same velocity.

Explanation :

Case 1 : Take two bodies , say of mass $$m_1$$ and $$m_2$$ ($$m_1 < m_2$$) and suppose both of them experience the same amount of force $$F$$. Then from Newton's second law

$$F = ma$$

So,

$$a= \frac{F}{m}$$

You can notice that if you keep $$F$$ constant and change the denominator $$m$$ (either increase or decrease) , you will get different values of acceleration (i.e. $$a_1 > a_2$$) .

So acceleration is inversely proportional to mass when $$F$$ is constant.

Case 2 : But if you apply different forces on the two bodies , i.e. if $$m_1$$ is half of $$m_2$$ then $$F_1$$ is also half of $$F_2$$ then the two bodies of different mass will have the same acceleration . This is what happens with the force of gravity , it increases proportionally with mass and thus all bodies of different mass have the same acceleration ($$g$$).

Now , since acceleration may be same or different, same is with velocity of the bodies after time $$t$$ (taking the initial state of the masses same).

Hope it helps ☺️.