← Newton's second and third laws

Solve for the acceleration

A 12 N net force acts on a 4.0 kg mass. How large is the acceleration?

You have the equation: a = F_net/m.

This lesson is practice. Given the net force on an object and its mass, you calculate its acceleration, quickly and the same way every time.

Every solve runs the same four steps: write down the values and mark the unknown, write down the equation, substitute in the values, simplify.

QuantityValueF_net12 Nm4.0 kga?
Step one, every time: write down the values and mark the unknown.

With F_net in newtons and m in kilograms, the acceleration comes out in m/s².

StepLineequationa = F_net/msubstitutea = 12 ÷ 4.0simplifya = 3.0 m/s²
Equation, substitution, result: the same three lines in every solve.

One check before any arithmetic: make sure the force you were given is the net force. In this lesson's questions, it is.

To find an acceleration, write down the values, write down a = F_net/m, then substitute and simplify. The answer's unit is m/s².

A 12 N net force acts on a 4.0 kg mass. Calculate the acceleration.

Write down the values in the question:

F_net = 12 N

m = 4.0 kg

a = ?

Write down the equation:

a = F_net/m

Substitute in the values:

a = 12 ÷ 4.0

Simplify:

a = 3.0 m/s²

The acceleration is 3.0 m/s².

The net force on an 18 kg loaded wheelbarrow is 63 N. Calculate its acceleration.

Write down the values in the question:

F_net = 63 N

m = 18 kg

a = ?

Write down the equation:

a = F_net/m

Substitute in the values:

a = 63 ÷ 18

Simplify:

a = 3.5 m/s²

The wheelbarrow's acceleration is 3.5 m/s².

Quick-fire drill

The net force on a 15 kg cart is 36 N. Enter the cart's acceleration in m/s².

The net force on a 12 kg wagon is 54 N. Enter the wagon's acceleration in m/s².

The net force on a 6.0 kg toolbox sliding on a workbench is 9.0 N. Enter its acceleration in m/s².

The net force on a 56 kg crate is 140 N. Enter the crate's acceleration in m/s².

The net force on a 15 kg canoe being paddled hard is 33 N. Enter its acceleration in m/s².

A golf cart carrying two riders has a total mass of 500 kg. Driving away from the clubhouse, the net force on it is 850 N forward. Enter its acceleration in m/s².

Your turn

The net force on an 8.0 kg sled is 44 N. Enter the sled's acceleration in m/s².

A cyclist and bicycle have a combined mass of 75 kg. Sprinting from the start line, the net force on them is 240 N. Enter the acceleration in m/s².

A remote-controlled car has a mass of 2.8 kg. Leaving the starting gate, the net force on it is 21 N forward. Enter its acceleration in m/s².