Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Linked: F = ma questions · Resultant forces notes
✏️ Work on paper. For every question, draw the object with its force arrows first. Then open the answer.
📌 KEY DEFINITIONS – learn them word for word
Resultant force: the single force that has the same effect as all the forces acting on an object together.
Newton’s second law: the acceleration of an object is directly proportional to the resultant force acting on it, and inversely proportional to its mass (F = ma).
The F in F = ma is always the resultant force – never just one of the forces.
🧮 Three steps every time
Step 1 – Draw it. Draw the object as a box. Add an arrow for each force and write the size on it.
Step 2 – Find the resultant force.
Forces in the same direction: add them.
Forces in opposite directions: take away the smaller from the bigger.
The resultant acts in the direction of the bigger side.
Step 3 – Use F = ma.
Acceleration = resultant force ÷ mass (a = F ÷ m)
Units: force in N, mass in kg, acceleration in m/s².
Level 1: Two forces, opposite directions
Q1 (F) 🛒 Shopping trolley. You push a trolley forwards with a force of 30 N. Friction acts backwards with a force of 10 N. The trolley has a mass of 20 kg. Calculate its acceleration.
Show answer
Resultant force = 30 − 10 = 20 N forwards
Acceleration = 20 ÷ 20 = 1 m/s²
Q2 (F) 🚗 Car pulling away. A car’s engine gives a driving force of 3000 N. Friction and air resistance together are 1000 N. The car has a mass of 1000 kg. Calculate its acceleration.
Show answer
Resultant force = 3000 − 1000 = 2000 N forwards
Acceleration = 2000 ÷ 1000 = 2 m/s²
Q3 (F) 🪂 Skydiver just after jumping. A skydiver has a weight of 800 N. Air resistance on her is 200 N. Her mass is 80 kg. Calculate her acceleration.
Show answer
Resultant force = 800 − 200 = 600 N downwards
Acceleration = 600 ÷ 80 = 7.5 m/s²
Level 2: More than two forces
Q4 (F) 🚲 Cyclist. A cyclist pedals with a forward force of 250 N. Air resistance is 100 N and friction is 30 N. Both act backwards. The cyclist and bike have a total mass of 75 kg. Calculate the acceleration.
Show answer
Total backwards force = 100 + 30 = 130 N (same direction, so add)
Resultant force = 250 − 130 = 120 N forwards
Acceleration = 120 ÷ 75 = 1.6 m/s²
Q5 (F) 🚙 Pushing a broken-down car. Two friends push a car forwards. One pushes with 200 N and the other with 250 N. Friction acts backwards with a force of 150 N. The car has a mass of 600 kg. Calculate its acceleration.
Show answer
Total forwards force = 200 + 250 = 450 N (same direction, so add)
Resultant force = 450 − 150 = 300 N forwards
Acceleration = 300 ÷ 600 = 0.5 m/s²
Q6 (F) 🚤 Trick question – speedboat. A speedboat’s engine gives a forward force of 5000 N. Water resistance and air resistance together are 5000 N. The boat has a mass of 2000 kg. Calculate its acceleration. What is the boat doing?
Show answer
Resultant force = 5000 − 5000 = 0 N
Acceleration = 0 ÷ 2000 = 0 m/s²
The forces are balanced, so the boat moves at a constant speed (it has not stopped).
Level 3: Slowing down and going up
Q7 (F/H) 🛑 Emergency stop. A driver takes her foot off the accelerator and brakes hard. There is now no driving force. The braking force is 4500 N and air resistance is 500 N. Both act backwards. The car has a mass of 1000 kg. Calculate the deceleration.
Show answer
Resultant force = 4500 + 500 = 5000 N backwards (both backwards, so add)
Deceleration = 5000 ÷ 1000 = 5 m/s²
Q8 (F/H) 🚀 Rocket launch. A small rocket has a mass of 2000 kg. Its engines push it up with a thrust of 30 000 N. Its weight is 20 000 N. Calculate its acceleration as it lifts off.
Show answer
Resultant force = 30 000 − 20 000 = 10 000 N upwards
Acceleration = 10 000 ÷ 2000 = 5 m/s²
Level 4: Challenge (H)
Q9 (H) 🪂 Find the weight first. A skydiver has a mass of 70 kg. Just after she jumps, air resistance on her is 300 N. Gravitational field strength = 9.8 N/kg. Calculate her acceleration to 2 significant figures.
Show answer
Step 1 – Weight = mass × g = 70 × 9.8 = 686 N downwards
Step 2 – Resultant force = 686 − 300 = 386 N downwards
Step 3 – Acceleration = 386 ÷ 70 = 5.51… = 5.5 m/s²
Q10 (H) 🚚 Work backwards. A lorry has a mass of 12 000 kg. It accelerates at 0.5 m/s². Friction and air resistance together are 2000 N. Calculate the driving force from the engine.
Show answer
Step 1 – Resultant force = m × a = 12 000 × 0.5 = 6000 N
Step 2 – The engine must beat the 2000 N resistance and give a 6000 N resultant.
Driving force = 6000 + 2000 = 8000 N
⚠️ Where students lose marks
- Putting the biggest force into F = ma instead of the resultant force. Always find the resultant first.
- Forgetting to add forces that act in the same direction (like air resistance + friction).
- Thinking a resultant force of 0 means the object has stopped. It means constant speed.
- Mixing up mass (kg) and weight (N). Weight = mass × 9.8.
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