# How does the acceleration of a cart depend on the total mass if the net force is constant? The answer above is correct: if the force is constant, the mass is inversely proportional to the acceleration. So if the mass increases, the acceleration decreases, and vice versa.

This comes from the second Newton's Law, that states that the net force equals mass times acceleration:

`F = m_1*a_1` , where `m_1` is the original mass and `a_1` is the original acceleration.

If the mass and acceleration change, but the force remains the same, then

`F = m_2*a_2` , where `m_2` is the new mass and `a_2` is the new acceleration.

Combining the two equations, we get

`m_1*a_1 = m_2*a_2`

If we divide this equation by `m_1*a_2` , it becomes

`a_1/a_2 = m_2/m_1` ,

which means that the acceleration is inversely proportional to mass.

This is why mass is also called "the measure of inertia". Inertia is the tendency of an object to resist the change in its motion, or the change in how fast it moves. The objects with larger mass have larger inertia, so they are harder to accelerate.

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Approved by eNotes Editorial Team By Newton's Second Law, the acceleration of an object is proportional to the net force and inversely proportional to the mass:

a = Fnet/m

If Fnet is a constant, then as m increases a will decrease and as m decreases a will increase proportionally.  That is, doubling the mass cuts the acceleration in half.  Halving the mass doubles the acceleration.