Calculating speed

Speed (m/s) = Distance travelled (m) / Time taken (s)

If you measure average speed over a very short time interval, you get very close to a value for instantaneous speed (the speed at a particular moment in time).

Displacement is expressed as distance with a direction and measures the distance moved in a specific direction. It is a vector quantity-it has a size (magnitude) and a direction.


The velocity of an object is its speed in a certain direction. It is also a vector quantity.

Average velocity (m/s) = Displacement (m) / Time taken (s)

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Distance-time graphs vs Displacement-time graphs

Distance-time graphs:

A distance time graph can be used to visualise a journey. The time for the journey is plotted on the x axis and the distance travelled is plotted on the y axis. A straight line means that the vehicle is travelling at a constant speed. A horizontal line means that the vehicle has stopped stationary. The gradient of a line on the graph is equal to the speed. The steeper the gradient, the faster the speed. A curved line means that the speed is changing.

Displacement-time graphs:

Return journeys can be visualised on a displacement time graph. When the vehicle has returned to its starting point its displacement will be zero. The displacement would be negative if the vehicle travelled behind its starting point.

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The rate at which the speed of an object increases is known as acceleration. It is measured in metres per second squared (m/s2).

Acceleration (m/s2) = change in speed (m/s) / time taken (s).

When an object slows down it has a negative acceleration that is sometimes called deceleration or retardation. There has to be a net force acting on an object to cause acceleration or deceleration. When the net or overall force is zero, the acceleration is zero.

A vehicle travelling at constant speed around a corner is changing its velocity. Acceleration is defined as the rate of change of velocity.

Acceleration (m/s2) = change in velocity (m/s) / time taken (s)

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Speed-time graphs vs Velocity-time graphs

A speed-time graph is used to show the changes in speed during a journey. Speed is plotted on the y axis and the time on the x axis. A horizontal line means that the speed of the object is constant. If the horizontal line is along the x axis then the speed is zero and the object is stationary. A straight line going up shows acceleration and a straight line going down shows deceleration. The steeper the line, the greater the size of the acceleration or deceleration.

The instantaneous speed of a vehicle in a certain direction is its instantaneous velocity.

A velocity-time graph also shows the direction in which an object is travelling. A positive velocity means that the object travels in a certain direction and a negative velocity means that the object is travelling in the opposite direction. The gradient of the velocity-time graph is equal to the acceleration.

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Forces between objects

A force is a push or pull that acts between two objects. A force arises from an interaction between two objects. They always act in pairs. A repulsive force pushes objects apart; an attractive force pulls objects towards each other. The size of the force is always the same on both objects. The force on each object acts in the opposite direction to each other. When you stand you push downwards on the floor. The force is equal to your weight. At the same time, the ground exerts an upwards force on you (this is called the reaction force). It stops gravity from pulling you through the floor. The reaction force is equal and opposite to your weight, so you are not accelerating up or down; the reaction force just balances your weight. If you jump upwards, you need to push harder on the floor- the reaction force increases. Now the forces are unbalanced and you will accelerate upwards. 

(http://www.bbc.co.uk/staticarchive/9db0c22dbd8ec3a3c905dc8a854168e44c14035e.gif)Forces are vector quantities; they have magnitude (size) and direction. A force is represented by an arrow on a diagram.

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Friction is a force which acts between two surfaces. As the two surfaces slide over each other, friction acts to oppose the motion. The size of the friction depends on the roughness of the surfaces and how hard the surfaces are pushed together (the heavier the object the more friction). 

When you try to push an object along a surface, friction will be equal to the applied force and acts in the opposite direction so the object will not move. As you increase the applied force, the friction will increase too. Eventually, the friction reaches a maximum level and the object will start to move. This is called limiting friction. 

The kinetic energy of the moving object is transferred to heat energy in both surfaces. Lubrication (oil) is used to reduce the friction between moving parts of machinery to stop them getting too hot and wearing out. 

You need friction in order to walk. When you walk your feet push against the friction on the floor, so the floor pushes your foot forwards. The resultant force acting between your foot and the floor is a combination of friction and the reaction of the surface. These forces combine to push the foot in a diagonal upwards direction.

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Resultant force

There are usually several forces acting on an object at the same time. The resultant force is the total or overall force acting on an object. When you add forces together you must account for both the size and the direction of the force. When the resultant force is equal to zero the forces are balanced and the object will carry on moving in a straight line at a constant speed. In a frictionless space, once an object starts moving it should keep moving at the same speed. When the forces are unbalanced, there is a net force on the object and it will speed up, slow down or change direction. 

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Terminal velocity

Objects falling accelerate towards the ground at 9.8m/s2, due to gravity. The force of gravity always acts towards the centre of the earth. The atmosphere creates an upwards force that slows down falling objects. This is knwon as air resistance or drag. Drag acts in the opposite direction to the speed (or velocity) of the object. Drag force is increased as the speed of the object increases. The larger the surface area of the object, the larger the drag force. 

The constant maximum speed reached by a falling object is known as its terminal velocity. The ideas about terminal velocity work in the same way for vehicles, with friction and drag acting in the opposite direction to the driving force.

(See next card for picture)

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Terminal velocity


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Collisions and momentum

Large forces are exerted during collisions. The size of the force depends on:

  • the mass of the object (the heavier the object, the larger the force)
  • the speed (or velocity) of the object (the faster the object, the larger the force)
  • the duration of the impact (the longer the time to stop, the lower the force)

Most car safety deices such as air bags, seat belts, crumple zones and crash helmets are designed to increase the impact time, thus reducing the force in a collision. 

Momentum (kg m/s) = mass (kg) x velocity (m/s)

A resultant force will change an object's momentum . The larger the force exerted, the larger the change in momentum.

Change in momentum (kg m/s) = resultant force (N) x time for which it acts (s)

Force is equal to the rate of change of momentum: Force = change in momentum / time taken 

Momentum is a vector quantity since it has both direction and magnitude.

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Work & Potential energy

WORK: The energy used by the movement of a force is known as the work done. Energy and work are both measured in joules. Energy is defined as the ability to do work. 

Work done (J) = Force (N) x Distance moved in the direction of the force (m)

When work is done on an object, energy is transferred to that object. When work is done by an object, energy is transferred from the object to something else. 

Amount of enrgy transferred (J) = Work done (J)

All forms of energy have the potential to do work. Energy from food is transferred in our bodies so we can do exercise. Not all energy is transferred as work- some is dissipated as heat. 

GRAVITATIONAL POTENTIAL ENERGY (GPE): When you lift an object you do work against gravity. 1 joule of work will lift a weight of 1 newton a distnace of 1 metre. The work is transferred to GPE of the object. As an object is raised, its GPE increases; as it falls, its GPE decreases.

Change in GPE (J) = weight (N) x vertical height difference (m)

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Kinetic energy & Energy transfers

Kinetic energy (KE):

When you push an object to get it moving (increase its velocity) you do work. The work is transferred to the moving object as KE. The greater the mass of the object and the faster its speed, the greater its KE.

Kinetic energy (J) = 12 × mass (kg) × (velocity)(m/s)

Energy transfers:

As a rollercoaster travels round its track, going up and down, its energy changes from KE to GPE. Its total energy at any time is the sum of its KE and GPE. When there are no resistive forces the total energy remains constant. This is known as the principle of the conservation of energy (energy cannot be created or destroyed; it can only transfer between objects or change its form).

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this is p3

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