Motion and forces

Interpret H1 Physics motion graphs, use constant-acceleration equations and connect mass and momentum to Newton’s laws.

GCE A-Level H1 Physics 2027
3 lessons

Before you begin

This topic first describes motion and then explains it. The lessons start with motion graphs and the equations for constant acceleration, including free fall, then introduce mass and momentum, and finish with Newton’s three laws, which link the resultant force on a body to the change in its motion.

Be comfortable with: resolving vectors, because forces, velocities and accelerations are vectors, and identifying forces.

Learning goals

Interpret position, displacement, velocity and acceleration using equations and graphs.
Derive the uniformly accelerated motion equations from the definitions of velocity and acceleration.
Derive and apply uniformly accelerated motion equations with a stated sign convention.
Explain inertia and momentum, then apply Newton's laws using free-body diagrams.
State and apply Newton's three laws of motion

Syllabus statements covered

show an understanding of and use the terms position, distance, displacement, speed, velocity and acceleration
use graphical methods to represent distance, displacement, speed, velocity and acceleration
identify and use the physical quantities from the gradients of position-time or displacement-time graphs and areas under and gradients of velocity-time graphs, including cases of non-uniform acceleration
derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line
solve problems using equations which represent uniformly accelerated motion in a straight line, e.g. for bodies falling vertically without air resistance in a uniform gravitational field
show an understanding that mass is the property of a body which resists change in motion (inertia)
define and use linear momentum as the product of mass and velocity
state and apply each of Newton’s laws of motion: 1st law: a body at rest will stay at rest, and a body in motion will continue to move at constant velocity, unless acted on by a resultant external force; 2nd law: the rate of change of momentum of a body is (directly) proportional to the resultant force acting on the body and is in the same direction as the resultant force; and 3rd law: the force exerted by one body on a second body is equal in magnitude and opposite in direction to the force simultaneously exerted by the second body on the first body
recall the relationship resultant force F = ma, for a body of constant mass, and use this to solve problems

Lessons

Work through them in order.

Practise and check

Or choose

Topic reference

Quick reference

Idea	Relationship	Note
displacement–time graph	gradient = velocity	use the tangent on a curve
velocity–time graph	gradient = acceleration; area = displacement	area below the axis is negative displacement
constant acceleration	v = u + at, s = (1/2)(u + v)t	only while a is constant
	s = ut + (1/2)at², v² = u² + 2as
free fall	a = g = 9.81 m s⁻² downwards	no air resistance
momentum	p = mv	vector; unit kg m s⁻¹
Newton’s second law	F = (Δ p)/(Δ t); F = ma for constant mass	F is the resultant force

Core knowledge to remember

Displacement is the change in position, with a direction; distance is the total path length. Velocity is the rate of change of displacement, and acceleration is the rate of change of velocity.
The gradient of a displacement–time graph is the velocity; the gradient of a velocity–time graph is the acceleration; the area under a velocity–time graph is the displacement.
Mass is the property of a body that resists a change in its motion (inertia).
Linear momentum is the product of mass and velocity.
Newton’s first law: a body at rest stays at rest, and a body in motion continues to move at constant velocity, unless acted on by a resultant external force.
Newton’s second law: the rate of change of momentum of a body is proportional to the resultant force acting on it and is in the direction of the resultant force.
Newton’s third law: the force exerted by one body on a second body is equal in magnitude and opposite in direction to the force exerted at the same time by the second body on the first.

Common mistakes

Taking the total area under a velocity–time graph as the distance when part of it lies below the axis.
Using the constant-acceleration equations when the acceleration changes.
Thinking a thrown object has zero acceleration at its highest point.
Confusing mass with weight, or momentum with kinetic energy.
Using one force instead of the resultant force in F = ma.
Treating weight and the normal contact force on one body as a third-law pair, or cancelling a third-law pair on one free-body diagram.