Speed and Velocity
- Speed tells you how far an object will travel in a certain time but it does not tell you the direction of travel.
- Velocity tells you an object's speed and gives an indication of its direction of travel.
- To calculate the speed of an object you need to know the distance it has travelled and the time it took to travel that distance.
- Speed is calculated using the following formula:
Speed (m/s) = distance travelled (m)
time taken (s)
- It calculates an average speed over the total distance travlled, even if the speed of an object is not constant.
- The speed of an object at a particular point in time is called the instantaneous speed.
- Distance-time graphs show how the distance travelled by an object changes with time.
- The slope or gradient is a measure of the speed of an object. The steeper the slope, the greater the speed.
- If a line is horizontal, the object is stationary.
- Distance-time graphs can also be drawn as displacement-time graphs, where the displacement of an object is its net distance from its starting point together with an indication of direction.
- The acceleration of an object is the rate at which its velocity changes (measure of how quickly an object speeds up or slows down)
- To work out the acceleration of any moving object you need to know the change in velocity and the time taken for this change in velocity.
- The formula for acceleration is:
Acceleration (m/s squared) change in velocity (m/s)
(or deceleration) = time taken for change (s)
- Acceleration of an object is represented by the slope of a speed-time graph; the steeper the slope, the greater the acceleration.
- Velocity-time graph show how the velocity at which an object is moving changes with time. Velocity has a direction so if moving in a straight line in one direction is a positive velocity, then moving in a straight line in the opposite direction would be a negative velocity.
- A force occurs when two objects interact with each other.
- When one object exerts a force on another, it always experiences an equal and opposite force in return.
- The forces in an interaction pair are equal in size and opposite in direction.
- An example is gravity (weight) - two masses are attracted to each other e.g. we are attracted to the Earth and the Earth is attracted to us with an equal and opposite force but we do not notice the attraction of the Earth because it has such a big mass that our force has very little effect on it.
- Some forces, such as friction and reaction (of a surface), only occur in response to another force.
- An object is being pulled down to the surface by gravity and the surface pushes up with an equal force called the reaction of the surface.
- When two objects try to slide past one another, both objects experience friction that tries to stop them from moving.
Forces and Motion
- Arrows are used when drawing diagrams of forces.
- The size of the arrow represents the size of the force.
- The direction of the arrow represents the direction of the force.
- Force arrows are always drawn with the tail of the arrow touching the object.
- If more than one force acts on an object, the forces need to be added, taing the direction into account.
- The overall effect of adding all these forces is called the resultant force.
- A person walking, cars and bikes have a driving force.
- A car's driving force is produced by the engine.
- The person's muscles provide the driving force for someone walking or cycling.
- But, there is also a counter force caused by friction and air resistance which makes the vehicle slow down or stop.
- If the driving force is bigger than the counter force, the vehicle accelerates.
- If the driving force and counter force are equal, the vehicle travels in a straight line at a constant speed.
- If the counter force is bigger than the driving force, the vehicle decelerates.
- Falling objects experience two forces; the downward force of weight (which always stays the same) and the upward force of air resistance.
- When a skydiver jumps out of an aeroplane, the speed of the descent can be considered in two different parts - before and after the parachute opens.
Before the parachute opens
- When the skydiver jumps, he initially accelerates due to the force of gravity.
- However, as the skydiver falls he experiences the frictional force of air resistance in the opposite direction but its not as great as gravity so he continues to accelerate.
- As his speed increases, so does the air resistance acting on him until finally the forces are equal which means that the resultant force on him is now zero and hs falling speed becomes constant. This speed is called the terminal velocity.
After the parachute opens
- The air resistance is bigger than the gravity which decreases his speed, decreasing his air resistance also until they are eventually equal,he is at a new terminal velocity until he lands.
- Momentum is a measure if the motion of an object. It is calculated using the following formula:
momentum (kg m/s) = mass (kg) X velocity (m/s)
- If the resultant force on an object is zero its momentum will not change. If the object is stationary, it remains stationary. If it's already moving, it will continue moving in a straight line at a steady speed.
- If the resultant force on an object is not zero it causes a change in momentum in the direction of the force. This could give a stationary object momentum (make it move) and increase or decrease the speed or change the direction of a moving object (change the velocity).
- The size of the change in momentum depends on the size of the resultant force and the length of time the force is acting on the object.
- If a car is involved in a collision it comes to a sudden stop (undergoes a change in momentum)
- If this change in momentum is spread out over a longer period of time, the average resultant force acting on the car will be smaller.
Kinetic and GPE Energy
- A moving object has kinetic energy. The amount of kinetic energy an object has depends on the mass and the velocity of the object.
- The greater the mass or velocity, the more kinetic energy it has. Therefore, it takes longer to stop a heavy, fast-moving object, than a light slow-moving object.
- Car brakes convert kinetic energy into heat energy. Amount of energy stays the same.
- Kinetic energy is calculated using the following formula:
kinetic energy (joules, J) = 1/2 X mass (kilograms, kg) X velocity squared (m/s squared)
- An object lifted above the ground gains potential energy (PE), often called gravitational potential energy (GPE).
- The additional height gives it the potential to do work when it falls (e.g a diver on diving board)
- It is calculated by the following formula:
change in GPE (joules, J) = weight (newtons, N) X vertical height difference (metres, m)
- If an object is dropped, it's gravitational potential energy decreases and is conveted into kinetic energy.
Work and Energy
- When a force moves an object, work is done on the object resuting in the transfer of energy.
- When work is done by an object it loses energy and when work is done on an object it gains energy according to the relationship:
amount of energy transferred (joules, J) = work done (joules, J)
- When a force acting on an object causes it to accelerate, work is done on the object to increase its kinetic energy.
- If we ignore the effects of air resistance and friction, the increase in kinetic energy will be equal to the amount of work done However, in reality some energy is dissipated (lost) as heat and the increase in kinetic energy will be less than the work done.
- When a car is travelling at a constant speed the driving force from the engine is balanced by the counter force. All of the work being done by the engine is used to overcome friction and there is no increase in kinetic energy.
- Work done is calculated by the following formula:
work done by a force (joules, J) = force (newtons, N) X distance moved by the force (metres, m)