area metre-squared (m2)

distance metre (m)

acceleration metre/second-squared (m/s2)

speed  metre/second (m/s)

velocity metre/second (m/s)

time  second (s)

Speed does not involve direction. Speed is a scalar quantity.

The speed of a moving object is rarely constant. When people walk, run or travel in a car their speed is constantly changing.

The speed at which a person can walk, run or cycle depends on many factors including: age, terrain, fitness and distance travelled.

Typical values may be taken as:

• walking ̴1.5 m/s
• running ̴3 m/s
• cycling ̴6 m/s.

A typical value for the speed of sound in air is 330 m/s.

For an object moving at constant speed the distance travelled in a specific time can be calculated using the equation:

distance travelled = speed × time

distance travelled = speed × time

4 = speed x 3

speed = 4 / 3

The speed of the object is 1.3 m/s

distance travelled = speed × time

distance travelled = 13 x 0.6

The thinking distance is 7.8 m

The velocity of an object is its speed in a given direction. Velocity is a vector quantity.

Displacement is distance with a direction. Displacement is a vector.

Acceleration is a change in speed and/or direction.

learn this definition

Motion in a circle involves constant speed but changing velocity because the direction is always changing

If an object moves along a straight line, the distance travelled can be represented by a distance–time graph.

## Distance-Time Graphs

The speed of an object can be calculated from the gradient of its distance–time graph.

If an object is accelerating, its speed at any particular time can be determined by drawing a tangent and measuring the gradient of the distance–time graph at that time.

The speed is the gradient of the line

gradient = 250 – 0 / 50 – 0

The speed = 5 m/s

draw a tangent

at 20 minutes

measure the gradient of the tangent

## Average Acceleration (unit: m/s2)

The average acceleration of an object can be calculated using the equation:

acceleration = change in velocity / time taken

or

acceleration = (final velocity – initial velocity) / time taken

An object that slows down is decelerating.

acceleration = (final velocity – initial velocity) / time taken

acceleration = (11.6 – 0)/3.2

The acceleration is 3.625m/s2

## Uniform Acceleration over a Distance (unit: m/s2)

The following equation applies to uniform acceleration:

final velocity² − initial velocity² = 2 × acceleration × distance

final velocity² − initial velocity² = 2 × acceleration × distance

192 – initial velocity2 = 2 x 2 x 84

361- initial velocity2 = 336

361 – 336 = initial velocity2

25 = initial velocity2

The initial velocity is 5 m/s

## Velocity-Time Graphs

The acceleration of an object can be calculated from the gradient of a velocity–time graph.

The distance travelled by an object (or displacement of an object) can be calculated from the area under a velocity–time graph.

The distance travelled by an object (or displacement of an object) can be calculated from the area under a velocity–time graph.

If the graph is not a straight line, you can count the squares to find the area

Distance travelled by car A:

= (15 x 0.6) + (0.5 x 15 x 2.6)

distance travelled by A = 28.5 m

Distance travelled by car B:

= (15 x 1.4) + (0.5 x 15 x 2.6)

distance travelled by B = 40.5.

Extra distance travelled by B = 40.5 – 28.5 = 12m

## Falling Under Gravity

Near the Earth’s surface any object falling freely under gravity has an acceleration of about 9.8 m/s2

An object falling through a fluid initially accelerates due to the force of gravity.

As the falling object increases speed, the air resistance on it increases

When the air resistance = the weight, the forces acting on the object are balanced: there is no resultant force.

Eventually the resultant force will be zero and the object will move at its terminal velocity.

first terminal velocity

• on leaving the plane the only force acting is weight (downwards)
• as parachutist falls air resistance acts (upwards)accept drag / friction for air resistance
• weight greater than air resistance
• as velocity / speed increases so does air resistance
• terminal velocity reached when air resistance = weight

to explain second lower terminal velocity

• opening parachute increases surface area
• which air resistance
• air resistance is greater than weight
• resultant force acts upwards / opposite direction to motion
• parachutist decelerates / slows down
• the lower velocity means a reduced air resistanceair resistance and weight become equal but at a lower (terminal) velocity