Forces and motion is the bedrock of Newtonian mechanics. It underpins every dynamics topic at O-Level and explains everyday phenomena, from braking cars to satellite orbits.
The topic begins by describing motion with speed, velocity, acceleration and motion graphs. It then uses Newton's three laws, weight, free body diagrams and friction to explain how a resultant force changes an object's motion.
What these notes cover
- •Speed, velocity and acceleration
- •Scalars and vectors
- •Motion graphs (s-t and v-t)
- •Newton's First Law — Law of Inertia
- •Newton's Second Law
- •Newton's Third Law
- •Weight
- •Free body diagrams
- •Friction
- •Worked examples
- •Common mistakes
- •Summary
Key definitions
- Scalar
- A quantity with magnitude only, such as distance and speed.
- Vector
- A quantity with magnitude and direction, such as displacement and velocity.
- Inertia
- The resistance of an object to changes in its state of motion. Greater mass means greater inertia.
- Free body diagram (FBD)
- A diagram that isolates one object and shows every force acting on it as a labelled arrow originating from the object.
- Friction
- A contact force that opposes relative motion (or the tendency of motion) between two surfaces in contact. It acts parallel to the contact surface.
Key formulas
Average speed / velocity
v = s ÷ t
Gives average speed or average velocity over the time taken t (in s).
Acceleration
a = (v − u) ÷ t
u = initial velocity, v = final velocity, t = time taken (SI units: m/s, m/s², s). A negative value is a deceleration.
Newton's Second Law
Fₙₑₜ = ma
Fₙₑₜ is the resultant force (N), m is mass (kg), a is acceleration (m/s²). The acceleration is always in the direction of the resultant force.
Acceleration from resultant force
a = Fₙₑₜ ÷ m
Rearranged Second Law. Find the resultant force first, then divide by the mass.
Weight
W = mg
W is weight (N), m is mass (kg), g ≈ 10 N/kg near Earth's surface (use 9.81 if the question specifies).
Unit conversion
speed in m/s = speed in km/h ÷ 3.6
Convert km/h to m/s before substituting into a = (v − u) ÷ t.
Worked example
A 10 kg box is pushed to the right with 50 N. Friction of 20 N acts to the left. Find the acceleration.
- 1Take right as the positive direction.
- 2Find the resultant force: Fₙₑₜ = 50 − 20 = 30 N.
- 3Apply Newton's Second Law: a = Fₙₑₜ ÷ m = 30 ÷ 10 = 3.0 m/s².
- 4The box accelerates at 3.0 m/s² to the right.
Watch out: Do not substitute the 50 N applied force alone into Fₙₑₜ = ma. Always find the resultant force first.
Common mistakes
Mixing up mass and weight
Wrong: Treating mass and weight as the same quantity.
Right: Mass is measured in kg and is constant everywhere; weight W = mg is a force measured in N and depends on g.
Cancelling action-reaction pairs
Wrong: Assuming an action-reaction pair cancels out.
Right: Action-reaction pairs act on different objects, so they never cancel. Only forces on the same object sum to give the resultant.
Wrong friction direction
Wrong: Drawing friction opposite to the applied force by default.
Right: Friction always opposes the direction of motion (or tendency of motion) and acts parallel to the contact surface.
Questions students ask
What is the difference between mass and weight in physics?
Mass is measured in kg and does not change with location. Weight is a force measured in N, calculated using W = mg, where g ≈ 10 N/kg near Earth's surface.
Do action and reaction forces cancel each other out?
No. By Newton's Third Law, the two forces in an action-reaction pair are equal and opposite but act on different objects. Only forces acting on the same object add up to give the resultant force.
What does the area under a velocity-time graph represent?
The area under a v-t graph gives the displacement. The gradient of a v-t graph gives the acceleration, and a horizontal line means constant velocity.
What is the difference between static and kinetic friction?
Static friction prevents an object from starting to move, while kinetic friction acts while the object slides. Kinetic friction is generally smaller than maximum static friction.
In the full PDF
- •Velocity-time graph showing uniform acceleration, constant velocity and uniform deceleration
- •Labelled free body diagram of a pushed block with weight, normal force, applied force and friction
- •Step-by-step method for drawing a correct free body diagram
- •Two further worked examples: a block on a frictionless surface and a car accelerating from rest
- •The remaining common mistakes, including unit conversion and using a single force in Fₙₑₜ = ma
- •Five-point summary of the whole topic