# Newton's second law

1. Nov 25, 2008

### alpha372

1. The problem statement, all variables and given/known data
True or false:
"Given that the same force acts on particle A and B, If object B covers the same distance in less time than particle A, object B is less massive than object A"

2. Relevant equations
net force = mass(acceleration)

3. The attempt at a solution
I believe this is true because f = ma implies that m = f/a

Looking at m = f/a I find a conditional:
If acceleration is large, mass is small.

Looking at a= dv/dt I find another conditional:
If time gets small, acceleration gets large.

Putting these conditionals together in the statement m = f/a, I find the conditional:
As the interval of time decreases, the mass of the particle must decrease (assuming a constant force and distance).

Therefore, I find it safe to conclude that the original statement is true-- The original statement being:
"Given that the same force acts on particle A and B, If object B covers the same distance in less time than particle A, object B is less massive than object A".

2. Nov 25, 2008

### LowlyPion

I think your first observation is sufficient.

Since F is constant then a smaller mass will experience greater acceleration at all points. Since displacement is going to be proportional to acceleration at all time points then displacement is the larger for the larger acceleration.

x = 1/2*a*t2