01 / The Big IdeaPush something. Watch it speed up.
Imagine you give a shopping trolley a firm push. It accelerates. Now imagine the same push, but the trolley is loaded with bricks. It barely moves. Same push, different result.
That is everything Newton's Second Law is about. Two things decide how fast something accelerates: how hard you push it, and how heavy it is.
The same 10 N force produces ten times less acceleration on ten times the mass.
02 / The FormulaOne equation does all the work.
Newton put this idea into a single line of mathematics. It is one of the most important equations in IGCSE Physics.
F = m × a
F newtons (N) ·
m kilograms (kg) ·
a metres/sec² (m/s²)
The force is the resultant force, the total of all forces acting in one direction, after you have subtracted any forces acting in the opposite direction. This matters for the exam. If the question gives you two forces, you almost always need to find the resultant first.
Interactive Simulator
Calculate the Resultant Force
Mass (m) = 5.0 kg
Resultant Force (F) = Thrust - Drag = 30 - 10 = 20 N
Acceleration (a) = F / m = 4.00 m/s²(accelerating right)
03 / Worked ExampleForce on an accelerating car.
Example
A car of mass 1 200 kg accelerates from rest to 24 m/s in 8 seconds along a straight road. Calculate the resultant force on the car.
STEP 1 · Find the acceleration
Acceleration is the change in velocity divided by the time taken. a = (24 − 0) ÷ 8 = 3 m/s²
STEP 2 · Apply F = maF = 1 200 × 3 F = 3 600 N
Resultant force = 3 600 N (forward, along the road)
Notice the direction in the final answer. Cambridge often awards a separate mark for stating the direction. A bare number can cost you one mark.
Check Yourself
Quick recall: three questions
1. A 2 kg block accelerates at 4 m/s². What is the resultant force on it?
Correct. F = ma = 2 × 4 = 8 N. The most common mistake here is dividing instead of multiplying.
2. A 5 kg ball is pushed with a force of 20 N. Friction on the ball is 5 N. What is its acceleration?
Correct. Resultant force first: 20 − 5 = 15 N. Then a = F ÷ m = 15 ÷ 5 = 3 m/s². The trap was using 20 N directly without subtracting friction.
3. If the resultant force on an object is zero, the object will...
Correct. Zero resultant force means zero acceleration, but the object can still be moving, just at constant velocity. This is one of the most tested misconceptions in 0625.
04 / Past Paper StyleHow Cambridge actually asks this.
The question below is in the style of an IGCSE Physics 0625 Paper 4 (Extended) question. Try it before scrolling to the marking.
0625/42 · Style of May/June 2023 · Q3[ 4 marks ]
(a) A van of mass 1 500 kg is travelling at 12 m/s. The driver applies the brakes and the van decelerates uniformly, stopping in a distance of 18 m.
Calculate the average braking force acting on the van. [4]
Original question in the style of Cambridge Assessment International Education. Not reproduced from any specific past paper.
What the examiner wants
Four marks here means four distinct pieces of work, not just a number. The examiner is looking for: a kinematics equation to find a, the substitution, the application of F = ma, and the direction. Skip any step and you cap your marks at three.
M1
Use of v² = u² + 2as → 0 = 12² + 2 × a × 18, giving a = −4 m/s² (negative because decelerating)
M2
Correct substitution into F = ma: F = 1 500 × 4
M3
F = 6 000 N
M4
Direction stated: opposite to the motion of the van (or "backwards")
05 / The ApplicationTerminal velocity: F=ma in action.
As a skydiver falls, their weight (the downward force) remains constant. However, as they speed up, the air resistance (the upward drag force) increases.
Eventually, the upward air resistance exactly equals the downward weight. The resultant force becomes zero. According to F = ma, if F = 0, then a = 0. The skydiver stops accelerating and falls at a constant maximum speed, known as terminal velocity.
06 / Common MisconceptionsWhere students lose marks.
"A force keeps an object moving."
A force changes motion: it speeds up, slows down, or turns the object. An object can keep moving forever with no force on it (Newton's First Law). Confusing this costs marks on almost every motion question.
"Heavier objects fall faster."
In free fall (no air resistance), everything accelerates at the same rate, 9.8 m/s² near Earth. The greater weight on a heavier object is exactly cancelled by its greater mass when you apply F = ma. Air resistance is what creates the everyday illusion.
"If the resultant force is zero, the object must be at rest."
Zero resultant force means zero acceleration, not zero velocity. A car on cruise control at 60 mph has zero resultant force on it.