Question

If the force is double the acceletation will change by a factor of (assume the mass is constan)?

Answer 1

The acceleration will increase by a factor of two.

Explanation:

By Newton's second law, we know that the acceleration of an object is proportional to, and in the same direction as, the net force imparted upon that object. Mathematically, we know this as the familiar equation:

`vecF=mveca`

When the mass remains constant (usually the case), force and acceleration are directly proportional, i.e. if we increase one of these variables by an amount, the corresponding variable must also increase by this amount.

Therefore, if we double the force, we simultaneously double the acceleration.

Answer 2

The acceleration will double as well.

Explanation:

Consider the basic relationship (one dimension) between force and acceleration (Newton's Law):

`F=ma`

so that `a=F/m`

now let the force be `F'` where we have that `F'=2F`; we get (assuming the mass unchanged):

`F'=ma'`

rearranging:

`a'=(F') /m`

but: `F'=2F`; substitute:

`a'=2F/m` but we know that `a=F/m` and so:

`a'=2a`

we see that doubling the force causes the acceleration to double as well.