Extended · Practice questions · Newton's second law

Resultant force, mass, acceleration.

Six original Cambridge-style questions on F = ma: stating the law, the three rearrangements, and the step examiners reward most, finding the resultant force before you use it.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The step most students skip

F is the resultant force.

Find the resultant first: combine all forces (with direction) before using F = ma.
Three forms: F = ma, a = F ÷ m, m = F ÷ a.
No resultant, no acceleration: balanced forces mean constant velocity, not necessarily rest.

Analysis

[2 marks]

State Newton's second law as an equation, define each symbol, and give the unit of each quantity.

F = ma, where F is the resultant force (N), m is the mass (kg) and a is the acceleration (m/s²). ✓
A resultant force of 1 N gives a 1 kg mass an acceleration of 1 m/s². ✓

Calculation

[2 marks]

A resultant force acts on a 1500 kg car, giving it an acceleration of 2.0 m/s². Calculate the size of the resultant force.

F = ma = 1500 × 2.0

3000 N

Calculation

[2 marks]

A resultant force of 12 N acts on a 4.0 kg trolley. Calculate its acceleration.

a = F ÷ m = 12 ÷ 4.0

a = 3.0 m/s²

Calculation

[2 marks]

A resultant force of 200 N gives an object an acceleration of 5.0 m/s². Calculate the mass of the object.

m = F ÷ a = 200 ÷ 5.0

m = 40 kg

Calculation

[3 marks]

A 4.0 kg box is pushed along the floor with a forward force of 50 N. Friction provides a backward force of 30 N.

(a) Calculate the resultant force on the box.
(b) Calculate its acceleration.

(a) resultant = 50 − 30 = 20 N forward ✓

(b) a = F ÷ m = 20 ÷ 4.0

a = 5.0 m/s²

use the resultant 20 N, not the 50 N push

Analysis

[3 marks]

A car of mass 1200 kg has a forward driving force of 3000 N. The total resistive force (friction and air resistance) is 1200 N.

(a) Calculate the car's acceleration.
(b) The car speeds up. State and explain what happens to its acceleration as the resistive force grows.

(a) resultant = 3000 − 1200 = 1800 N a = F ÷ m = 1800 ÷ 1200

a = 1.5 m/s²

(b) As the car speeds up the resistive force increases, so the resultant force gets smaller. ✓
Since a = F ÷ m, a smaller resultant means a smaller acceleration; it falls towards zero at top speed. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.