A net force of 12 N acts on a 3 kg body. What is the acceleration?

Acceleration is force divided by mass. 12 divided by 3. 4 m/s², in the direction of the force

A 1200 kg car travelling at 20 m/s stops within 40 m. What force is needed?

The acceleration is zero squared minus 20 squared, over twice 40. Minus 400 over 80, so minus 5 m/s². The force is 1200 times 5. 6000 N, opposite to the motion

A ball thrown upwards is at the top of its flight. What is its acceleration?

At the top the speed is zero. But gravity is still acting. Acceleration follows the force, not the speed. About 10 m/s² downwards, exactly as at every other point

Newton's Laws · Grade 11

Does the net force set a body's speed, or its acceleration?

Its acceleration. The net force equals mass times acceleration, and the acceleration always points along the net force rather than along the velocity. So a constant force does not maintain a constant speed — it changes the speed at a constant rate — and a force perpendicular to the motion changes direction without changing speed.

Learning objectives

Calculate the acceleration of a body from the net force acting on it and from its mass
Find the net force needed to bring a moving body to rest within a given distance
Explain why the same force gives a loaded lorry a smaller acceleration than an empty one
Explain why the acceleration always points along the net force and not along the velocity

Three things the equation says

First: acceleration is proportional to force. Double the net force and the acceleration doubles, for the same mass.

Second: acceleration is inversely proportional to mass. The same force on twice the mass gives half the acceleration, which is why a loaded lorry accelerates more slowly than an empty one when the engine delivers the same force.

Third, and the most forgotten: the acceleration is along the net force. Not along the velocity, and not in the direction the body 'wants' to go. A ball thrown upwards is accelerating downwards the whole way, including while it is still rising.

Mass is resistance to change

The mass in the equation is not 'how much stuff' in the everyday sense but how much the body resists a change in its motion. That is the useful definition, and it is the one that explains why the same force moves a shopping trolley easily and a train barely at all.

Notice that weight does not appear here at all. Weight is a force, mass is a property of the body, and swapping them is the mistake that makes every Moon problem wrong.

Stopping within a given distance

A question that recurs in every exam: what force is needed to stop a moving body within a certain distance. The route does not go straight to the force — it goes through the acceleration.

First find the acceleration from a kinematic relation: final speed squared minus initial speed squared, divided by twice the distance. Then multiply by the mass to get the force.

That order is the whole technique: kinematics gives the acceleration, and Newton's second law converts it into a force. Jumping straight to the force leaves you without an equation.

Worked examples

A net force of 12 N acts on a 3 kg body. What is the acceleration?
1. Acceleration is force divided by mass
2. 12 divided by 3
Answer: 4 m/s², in the direction of the force
A 1200 kg car travelling at 20 m/s stops within 40 m. What force is needed?
1. The acceleration is zero squared minus 20 squared, over twice 40
2. Minus 400 over 80, so minus 5 m/s²
3. The force is 1200 times 5
Answer: 6000 N, opposite to the motion
A ball thrown upwards is at the top of its flight. What is its acceleration?
1. At the top the speed is zero
2. But gravity is still acting
3. Acceleration follows the force, not the speed
Answer: About 10 m/s² downwards, exactly as at every other point

Common mistakes

Assuming the acceleration is along the motion: It is along the net force. A rising ball accelerates downwards, and at the top of its flight the speed is zero while the acceleration is full.
Substituting weight for mass in the equation: The equation takes mass in kilograms. Putting in a weight in newtons multiplies the answer by about ten and wrecks every Moon problem.
Reaching for the force before the acceleration: Distance and speed give an acceleration, and only then does mass turn it into a force. Jumping to the force leaves an equation with two unknowns.

What to remember

Net force equals mass times acceleration.
Acceleration follows the force, not the velocity.
Mass is resistance to a change in motion.
Kinematics gives acceleration; the second law turns it into force.