Curriculum

OCR A Level Physics A H556

1. Development of Practical Skills in Physics

0/56

2. Foundations in Physics

0/29

3. Forces and Motion

0/108

4. Electrons, Waves and Photons

0/71

OCR H556 chapter questions and answers

0/2

Text lesson

2.1.1 Displacement, Velocity and Acceleration

2.1.1 Displacement, Velocity and Acceleration — AS PHYSICS 9702 notes: Define distance, displacement, speed, velocity and acceleration and use their equations and sign conventions.

1Distance

Distance a measure of how far an object travels; it is the total length of the path and is a scalar.

2Displacement

Displacement the change in position of an object, that is its distance from the starting position in a stated direction; it is a vector.

3Displacement is positive or negative

Displacement is positive or negative once a positive direction has been chosen, for example up or to the right.

A 300 m race on a 400 m track gives a distance of 300 m but a displacement of 100 m.

A full 400 m lap gives a displacement of zero.

Speed

Speed the distance an object travels per unit time; it is a scalar with magnitude only.

Average speed = total distance ÷ time taken.

SI unit m s⁻¹

SI unit m s⁻¹ other units such as km h^-1 or mph can be used when more appropriate.

A car's speedometer

A car's speedometer shows instantaneous speed.

Velocity

Velocity the rate of change of displacement; it is a vector and is speed in a given direction.

Average velocity vavg

Δs ÷ Δt

total displacement divided by total time.

For uniform acceleration

For uniform acceleration v_avg = (u + v) ÷ 2.

Instantaneous velocity

Instantaneous velocity the velocity at one moment, equal to the gradient of the tangent on a displacement-time graph.

Average velocity is not average speed in a given direction

Average velocity is not average speed in a given direction speed uses distance and velocity uses displacement,
- which can have very different magnitudes.

1Acceleration

Acceleration the rate of change of velocity; it is a vector.

Δv ÷ Δt = (v − u) ÷ t

What the symbols mean: a = acceleration (m s⁻²) · v = final velocity · u = initial velocity (m s⁻¹) · Δv = change in velocity · t = time taken (s)

u is the initial velocity and v is the final velocity, so Δv = v − u.

3SI unit m s⁻²

SI unit m s⁻² it describes how much the velocity changes every second.

4Acceleration can come from changing speed, changing direction or both

Acceleration can come from changing speed, changing direction or both a car at constant speed round a bend is accelerating.

1State the positive direction first

State the positive direction first and use signs consistently.

The sign of the acceleration is the sign of the change in velocity.

A trolley moving left and speeding up has increasingly negative velocity, so its acceleration is negative.

A trolley moving left and slowing down has positive acceleration.

4An object decelerates when its acceleration is opposite to its velocity

An object decelerates when its acceleration is opposite to its velocity this can be either sign.

5Zero velocity does not mean zero acceleration

Zero velocity does not mean zero acceleration at the top of a throw v = 0 but a = −9.8 m s^-2.

Uniform and non-uniform motion

Uniform motion

Uniform motion constant velocity with zero acceleration.

Uniformly accelerated motion

Uniformly accelerated motion constant acceleration.

Free fall near the Earth's surface without air resistance

Free fall near the Earth's surface without air resistance uniformly accelerated with g = 9.8 m s^-2 downward.

In most real situations the acceleration changes

In most real situations the acceleration changes use averages over an interval or instantaneous values from graphs.

The constant-acceleration equations

The constant-acceleration equations must never be used across a stage where acceleration changes.

Measuring motion

Two light gates a known distance apart

Two light gates a known distance apart or a single gate with a card of known length, with a data logger calculating v = length ÷ time.

Acceleration follows from two velocities and the time between them.

Ticker-timers and motion sensors

Ticker-timers and motion sensors give displacement against time directly.

Graphs of the data

Graphs of the data give velocity and acceleration as gradients and areas.

More from the specification

Velocity-time graph interpretation

The slope (gradient) of a velocity-time graph represents acceleration,
while the area under a straight or curved line equals the change in displacement,
which is a vector quantity.

Projectile motion components

For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s^-2

Kinematics of free fall

When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t²,
allowing experimental determination of the acceleration of free fall g.

Vector vs scalar distinctions

Displacement and velocity are vector quantities defined by both magnitude and direction,
whereas distance and speed are scalar quantities describing only magnitude.

Velocity-time graph interpretation

The slope (gradient) of a velocity-time graph represents acceleration,
while the area under a straight or curved line equals the change in displacement,
which is a vector quantity.

Projectile motion components

For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s^-2

Kinematics of free fall

When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t²,
allowing experimental determination of the acceleration of free fall g.

Vector vs scalar distinctions

Displacement and velocity are vector quantities defined by both magnitude and direction,
whereas distance and speed are scalar quantities describing only magnitude.

Velocity-time graph interpretation

The slope (gradient) of a velocity-time graph represents acceleration,
while the area under a straight or curved line equals the change in displacement,
which is a vector quantity.

Projectile motion components

For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s^-2

Kinematics of free fall

When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t²,
allowing experimental determination of the acceleration of free fall g.

Vector vs scalar distinctions

Displacement and velocity are vector quantities defined by both magnitude and direction,
whereas distance and speed are scalar quantities describing only magnitude.

Velocity-time graph interpretation

The slope (gradient) of a velocity-time graph represents acceleration,
while the area under a straight or curved line equals the change in displacement,
which is a vector quantity.

Projectile motion components

For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s^-2

Kinematics of free fall

When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t²,
allowing experimental determination of the acceleration of free fall g.

Vector vs scalar distinctions

Displacement and velocity are vector quantities defined by both magnitude and direction,
whereas distance and speed are scalar quantities describing only magnitude.

Projectile

Object moving under gravity alone in two dimensions.

Electromagnet

Magnet made by current through a coil around a magnetic core.

Velocity-time graph

A graph of velocity against time whose gradient is acceleration and area is displacement.

Kinematic equations

Equations relating displacement, velocity, acceleration and time for constant acceleration.

Acceleration-time graph

A graph of acceleration against time whose area is the change in velocity.

Projectile motion

Two-dimensional motion with constant horizontal velocity and vertical acceleration g.

Vector quantity

A quantity with both magnitude and direction.

Scalar quantity

A quantity with magnitude only, such as potential

Term	Meaning
Distance	The total length of the path travelled; a scalar.
Displacement	The change in position of an object with its direction; a vector.
Speed	The rate of change of distance.
Velocity	The rate of change of displacement.
Acceleration	The rate of change of velocity.
Instantaneous velocity	The velocity at a single moment in time.
Uniform acceleration	Acceleration that stays constant.
Deceleration	Acceleration opposite to the direction of the velocity.

Using distance instead of displacement when calculating velocity — check whether the direction reverses.

Thinking a negative acceleration always means slowing down — it depends on the sign of the velocity.

Assuming zero velocity means zero acceleration — at the top of a throw v = 0 but a = −9.8 m s^-2.

Forgetting that changing direction at constant speed is an acceleration.