Unbalanced force and acceleration (Newton's laws)

Key ideas

If the forces on an object balance (net force zero), its velocity doesn't change — it stays at rest or keeps moving at constant velocity.
If the forces are unbalanced, the object accelerates in the direction of the net force:

$F_{net} = ma$

Weight is the gravitational force on a mass: $F = mg$ , with $g = 9.8$ m s⁻² — straight down.

The tool for every force problem is a free-body diagram: the object, with every force on it drawn as a labelled arrow.

Free-body diagram of a box pushed across a floor, showing the support force upward, weight downward, applied force to the right, and friction to the left.

Worked ExampleAcceleration from a net force

A $1200$ kg car has a driving force of $3600$ N and total resistive forces of $600$ N. Find its acceleration.

Step 1 — Find the net force

Subtract the backward forces from the forward force:

$F_{net} = 3600 - 600 = 3000 \text{ N}$

Step 2 — Apply Newton's second law

$a = \frac{F_{net}}{m} = \frac{3000}{1200} = 2.5 \text{ m s}^{-2}$

Worked ExampleReading "constant velocity"

The same car later travels at a constant $25$ m s⁻¹. What is the driving force now?

Constant velocity means zero acceleration, so by $F_{net} = ma$ the net force is zero — the driving force exactly balances the $600$ N of resistance:

$F_{drive} = 600 \text{ N}$

Practice question

A $60$ kg runner accelerates at $1.5$ m s⁻². What net force does she experience? What is her weight?

Worked solution: $F_{net} = ma = 60 \times 1.5 = 90$ N forward. Weight $= mg = 60 \times 9.8 = 588 \approx 590$ N downward — note weight acts vertically and doesn't affect the horizontal net force here.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A $4.0$ kg trolley experiences a net force of $10$ N.

Show that its acceleration is $2.5$ m s⁻².

Merit

A $1200$ kg car has a forward driving force of $3000$ N and experiences $800$ N of resistance.

Calculate the car's acceleration, then state what the driving force must be for the car to travel at a constant velocity.

Excellence

A parachutist falls and eventually reaches a constant velocity (terminal velocity).

Describe and explain fully, using physics principles, why the parachutist's velocity becomes constant.