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Physics

Newton’s second law: find acceleration from net force

For a constant-mass object in an inertial frame, acceleration depends on the net force. Add the forces with their directions before dividing by mass.

Question

A 2 kg object is pulled horizontally to the right by 12 N. Friction is 2 N to the left, and there is no vertical acceleration. Find the horizontal acceleration, assuming these are the only horizontal forces.

Step by step

Take right as positive. The net force is 12 − 2 = 10 N. Use ΣF = ma, so a = 10 ÷ 2 = 5 m/s² to the right. The vertical normal force and weight balance under these assumptions.

a = ΣF / m = 10 N / 2 kg = 5 m/s²

Check your work

A newton equals kg·m/s², so dividing by kilograms gives m/s², not m/s. Dividing the pulling force alone by mass would give 6 m/s² and incorrectly ignore friction.

Try it yourself

If the object starts from rest and the acceleration stays constant for 3 seconds, v = v₀ + at = 0 + 5 × 3 = 15 m/s to the right. This is speed in a stated direction, not the distance travelled.

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