IB Physics HLTopic 1 — Motion, Forces & EnergyPaper 1 & 2F = ma & acceleration~9 min read
Newton’s Second Law
The first law told you when motion changes — only when there’s a resultant force. The second law tells you by how much. It ties the size of that resultant force to the acceleration it produces, through one of the most useful equations in all of physics: F = ma. Push harder and it accelerates more; load it heavier and it accelerates less.
📘 What you need to know
Newton’s second law: the resultant force on an object is directly proportional to its acceleration
As an equation: F = ma, where F is the resultant force (N), m is mass (kg), a is acceleration (m s−2)
A bigger resultant force gives a bigger acceleration; a bigger mass gives a smaller acceleration
Acceleration always acts in the same direction as the resultant force
The resultant force is the vector sum of all forces — find it first, then apply F = ma
A force along the motion speeds it up or slows it down; a force at an angle changes its direction
The equation
Newton’s second law of motion states:
Newton’s Second Law
The resultant force on an object is directly proportional to its acceleration
Written as an equation, that proportionality becomes:
Force, mass and accelerationF = ma
where F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m s−2). The equation packs in two everyday truths at once: for a given object, more force means more acceleration; and for a given force, more mass means less acceleration.
Same force, different mass. Double the mass and the acceleration halves — that’s a = F/m in a picture.
It’s always the resultant force
The F in F = ma is not any single force — it’s the resultant, the vector sum of everything acting on the object. So the routine is always the same: add up the forces to find the resultant, then divide by the mass to get the acceleration. And because force is a vector, the resultant can point either way along a line, which decides whether the object speeds up, slows down, or (below) accelerates the other way.
Taking right as positive, each cart’s resultant is just the forces added with signs. A positive resultant pushes right, a negative one pushes left, and equal opposing forces cancel to zero.
A resultant force that opposes the motion doesn’t send the object shooting backwards — it just makes it decelerate. Think of a car braking: the resultant points backward, the car slows, and only once it has stopped could it start moving the other way. Acceleration in the “negative” direction means “slowing down,” not “instantly reversing.”
Direction of acceleration
Acceleration is a vector, and it always points the same way as the resultant force. That gives you a quick read on what a force does:
F along motion → speeds up / slows down
F at an angle → changes direction
If the resultant force acts along the object’s line of motion, it changes the object’s speed. If it acts at an angle to the motion, it changes the object’s direction — the idea behind circular motion later in this topic.
🛠️ Using F = ma
Pick a positive direction — usually the direction the object is moving.
Add up all the forces with signs to find the resultant force F.
Divide by the mass:a = F ÷ m.
State the direction — the acceleration points the same way as the resultant force.
WE 1
A trolley of mass 1500 kg experiences a resultant force of 3750 N. Calculate its acceleration.
Step 1 — rearrange F = ma for acceleration
a = F ÷ m
Step 2 — substitute the valuesa = 3750 ÷ 1500a = 2.5 m s⁻²The acceleration points the same way as the 3750 N resultant force.
WE 2
A rocket of mass 3.0 × 105 kg produces an upward thrust of 12 MN. Its weight is 9 MN and, while climbing, air resistance acts on it with a force of 0.5 MN. Find the resultant force on the rocket and its acceleration.
Thrust (12 MN) is drawn longer than the two downward forces combined (9 + 0.5 MN), so the resultant points up — the rocket accelerates upward.
Step 1 — take up as positive, add the forcesF = 12 − 9 − 0.5 = 2.5 MN upward
= 2.5 × 10⁶ N
Step 2 — apply F = ma for acceleration
a = F ÷ m
a = (2.5 × 10⁶) ÷ (3.0 × 10⁵)a = 8.3 m s⁻² upwardPositive resultant → acceleration is upward, the same direction as the resultant force.
💡 Top tips
Find the resultant first. The F in F = ma is always the resultant — never plug in a single force before combining them.
Keep your signs consistent. Choose one positive direction and stick with it for the whole question.
Watch the units. Mass in kg, force in N, acceleration in m s−2. Convert kN or MN before substituting.
Always state a direction for the acceleration — it’s a vector, and it matches the resultant force.
Quick recap:F = ma links the resultant force to the acceleration it produces. More force means more acceleration; more mass means less. Always combine the forces into a resultant first, then divide by mass — and the acceleration points the same way as that resultant.
⚠ Common mistakes
Putting a single force into F = ma instead of the resultant of all the forces
Forgetting to convert kN or MN into N (or grams into kg) before substituting
Thinking a backward resultant force makes an object reverse instantly — it decelerates first
Leaving the acceleration as just a number and forgetting its direction
Mixing up the roles — dividing force by acceleration when you want a = F ÷ m
There’s one more piece to Newton’s picture. The first two laws deal with the forces on a single object; the third law is about what happens between two objects when they push on each other. That’s next: Newton’s Third Law and equal-and-opposite force pairs.
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