2.1
2.1.1 Define displacement, velocity, speed and acceleration
Displacement is the measured distance in a given direction. Velocity is the speed given in a direction (The ratio between the total displacement and the total time). Acceleration is the rate of change of velocity in a given direction. Speed is the rate at which a moving object covers a distance with respect to time. It is important to not mix up distance and displacement. If a person travels 3m to the north then 5m to the south, he has traveled a distance of 5+3=m. However, he has only displaced 2m southwards because he is only 2m away from his original point. The same with speed and velocity. If a person travels a distance of 8m in 10 seconds, then he has traveled at a speed of 8/10 = 0.8m/s. However, as in the above case he may have only displaced 2m. And therefore his velocity is 2/10 = 0.2m/s.
2.1.2 Explain the difference between instantaneous and average values of speed, velocity and acceleration
The instantaneous speed, velocity or acceleration is the speed, velocity or acceleration of a given object at that specific moment in time. The average speed is the ratio between the total distance covered and total time, the average velocity is the ratio between the total displacement and total time, and acceleration is the ratio between the total change in velocity over the relevant period of time. For example, if I traveled 10m in 10 seconds then my average speed would be 10/10 = 1m/s. However, I could have traveled 5m in the first second, took a 8second rest and traveled the next 5m during the 10th second. Therefore my instantaneous speed during the first and tenth second would be 5/1=5m/s, while my instantaneous speed during the period I was resting would be 0m/s.
2.1.3 State the conditions under which the equations for uniformly accelerated motion may be applied.
The equations for uniformly accelerated motion are:
1. v = u + at
2. s= 0.5 (u + v) t
3. s= ut + 0.5a(t^2)
4. s = vt - 0.5a(t^2)
5. v^2 = u^2 + 2as
6. a = (v - u)/t
Where u is the initial velocity of the object, v is the final velocity of the object, a is the acceleration of the object, t is the time period that is being concerned, and s is the total displacement. These equations will be given to you in the data booklet and therefore there is no need for you to memorise these. The conditions for you to be able to use this is that acceleration must be constant throughout the time period that is concerned.
2.1.4 Identify the acceleration of a body falling in a vacuum near the Earth's surface with the acceleration g of free fall.
The acceleration of a body falling in a vacuum near the Earth's surface with the acceleration of g is 9.81m/s^2.
2.1.5 Solve problems involving the equations of uniformly accelerated motion
You simply need to be able to identify which of the u, v, a, s and t are given, which of u, v, a, s and t you are required to calculate, identify which equation (refer to 2.1.3) you must use in order to calculate the value that is required, and substitute the values given in the question into the equations.
2.1.6 Describe the effects of air resistance on falling objects
The air resistance (or drag) is directly proportional to the velocity of the object provided that the density of air stays constant. Terminal velocity is when the air resistance is equal to the actual acceleration caused by gravity, causing the object to have no net acceleration. The shape and the mass of an object also affects the drag forced. You are often asked to draw two projectiles where one is affected by air resistance and the other is not. When it is a vertical projectile, the object with air resistance will simply not go up as high. If it is horizontal, it object with air resistance will land at a point closer to the original object. If it is launched at an angle, then you combine both of the previous ones to determine the projectile of the object with air resistance, i.e. it will not go up as high, and will not travel as far.
2.1.7 Draw and analyse distance-time graphs, displacement-time graphs, velocity-time graphs and acceleration-time graphs
When drawing these graphs, simply plot the data given to you. Time always goes on the x-axis and the other goes on the y-axis.
2.1.8 Calculate and interpret the slopes of displacement-time graphs and velocity-time graphs and the areas under velocity-time graphs and acceleration-time graphs
The gradient of a distance-time graph is the speed. The gradient of a displacement-time graph is the velocity. The area below a velocity-time graph is the total displacement while the gradient of a velocity-time graph is the acceleration. The area below an acceleration-time graph is the total change in velocity.
2.1.9 Determine relative velocity in one and in two dimensions
The relative velocity is the net velocity. Recall that velocity is the speed in a given direction. Therefore, in one dimension you have to determine in which direction the object is travelling and you must use the ratio between the displacement and time and not the ratio between speed and time. In two dimensions, you have to know the angle between the direction the object is travelling in, and the axis of the direction you are required to calculate the velocity in. You then multiply the speed of the object with the cosine of the angle to determine the velocity.
2.2
2.2.1 Calculate the weight of a body using the expression W=mg
The Weight of an object is the product of the objects' mass and the gravitational field strength (9.81N/kg on earth) at that point.
2.2.2 Identify the forces acting on an object and draw free-body diagrams representing the forces acting.
A force is something that can cause an object to change shape, or accelerate. When pulling spring, there is a tension force equal in magnitude against the direction you are pulling the string. When an object on Earth at rest. There must be a force acting against the gravitational force. For example, if your computer on your desk is stationary, there is a reaction force acting opposite to the direction of gravity allowing the computer to stay in place. Other forces you often must identify include friction, air resistance and forces causing an object to move. Warning: If an object is moving at a constant velocity, there is no net force on the object. In other words, if friction and air resistance can be ignored, you must conclude that there is no force applied to the object.
2.2.3 Determine the resultant force in different equations
Similar to 2.1.9 where you use trigonometry to find the resultant force. In these situations you simply use those equations to determine the force instead of velocity. If the forces are in one dimension, you simply need to add/subtract the numbers (add when the force is in the direction you want, subtract when it's the opposite).
2.2.4 State Newton's first law of motion
Every object continues in a state of rest of uniform motion in a straight line unless acted upon by an external force.
2.2.5 Describe examples of Newton's first law
If an object is moving at a constant velocity, there is no net force on the object. In other words, if friction and air resistance can be ignored, you must conclude that there is no force applied to the object. Basically, if an object has constant velocity, it is an example of Newton's first law in action.
2.2.6 State the condition for translational equilibrium
If an object is at rest, then it is in static equilibrium and, if it is moving with constant velocity, then it is in dynamic equilibrium. Newton's first law applies in both cases - the net force acting on the body is 0. This is the condition for translational equilibrium.
2.2.7 Solve problems involving translational equilibrium
Simply apply your knowledge from 2.2.1-2.2.6 to solve problems.
2.2.8 State Newton's second law of motion
F=ma. The net force acting on an object is the product of the objects' mass and the net acceleration of the object.
2.2.9 Solve problems involving Newton's first law
Two out of Force and acceleration will be given, and you will be required to determine the other. Some questions may require you to combine the equation with another one - for example a=v^2/r for circular motion (Refer to 2.4.3). This can be substituted for a in F=ma, giving F=mv^2/r.
2.2.10 Define linear momentum and impulse
Linear momentum (p) is equal to the product of the objects mass and its velocity - p=mv. The rate of change of momentum of a particle is directly proportional to the impressed force acting upon it and takes place in the direction of the impressed force. Impulse is the rate of change in momentum - F dt = dp. It is used in situations where the force acts for a significantly short time, such as kicking a ball.
2.2.11 Determine the impulse due to a time varying force by interpreting a force-time graph
The area under a force-time graph is the impulse
2.2.12 State the law of conservation of linear momentum
The law of conservation of linear momentum states that if the total external force acting on a system is zero then the momentum of the system remains constant.
2.2.13 Solve problems involving momentum and impulse
You always know that the total momentum before and after an even is the same if there is no external force acting on the system. By using this you can create an expression to determine certain unknown values.
2.2.14 State Newton's third law of motion
Newton's third law of motion states that when a force acts on a body, an equal and opposite force acts on another body somewhere in the universe.
2.2.15 Discuss examples of Newton's third law of motion
When a person jumps off the ground, the person exerts a force onto the ground to push himself upwards. At the same time, an equal and opposite reaction force is applied to the person by the earth as he jumps.
2.3
2.3.1 Outline what is meant by work
Work is the process of converting energy. It is equal to the product of the force applied and the distance it has moved.
2.3.2 Determine the work done by a non-constant force by interpreting a force-displacement graph. A typical example would be calculating the work done in extending a spring
The area below a Force-displacement graph is equal to the work done.
2.3.3 Solve problems involving the work done by a force
When attempting questions, notice that the known values given to you all relate to the force, distance or the work done. Use an appropriate formula (F=wd) calculate the values required from you in an exam.
2.3.4 Outline what is meant by kinetic energy
It is the energy that a body possesses by virtue of its motion. The kinetic energy of a body essentially tells you how much work the body is capable of doing. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. It is equal to 1/2*m*v^2
2.3.5 Outline what is meant by change in gravitational potential energy
The change in gravitational potential energy (for small values of h) is mgΔh. m is the mass of the object, g is the gravitational constant (in this chapter only small values of h is considered, and g is assumed to stay constant over the range of heights) and Δh is the change in height.
2.3.6 Sate the principle of conservation of energy
The principle of energy conservation states that the total amount of energy in an isolated system remains constant over time. When energy is not dissipated (energy converted into forms which are not desired) in a process, it is called a reversible process. However, this does not happen in reality as energy is converted into other forms such as heat and sound through friction and contact between bodies. The opposite is an irreversible process. Although energy is never lost, it can be degraded into types of energy that are less useful.
2.3.7 List different forms of energy and describe examples of the transformation of energy from one form to another
There are 4 different forms of energy. Thermal energy includes thermal energy, which is the kinetic energy of atoms and molecules. Chemical energy is the energy that is associated with the electronic structure of atoms and is therefore associated with the electromagnetic force. An example where chemical energy is converted into kinetic (thermal) energy is the combustion of carbon. Carbon combines with oxygen to release thermal energy along with light and sound energy. Nuclear energy is the energy that is associated with the nuclear structure of atoms and is therefore associated with the strong force. An example is the splitting of uranium nuclei by neutrons to produce energy. Electrical energy is associated with electric current. Boiling water can turn a turbine with a magnet which rotates in a coil to induce electrical energy. All of these fall into the category of potential or kinetic energy.
2.3.8 Distinguish between elastic and inelastic collisions
An elastic collision is when there is no mechanical energy that is lost. In other words, the total kinetic energy of the objects is the same before and after the collision. An inelastic collision is where mechanical energy is lost. Almost always in reality collisions are inelastic as energy is lost as sound and friction.
2.3.9 Define power
Power is the rate at which work is done. i.e. Work/time. The unit is joules per second, or Watt. Power is also equal to the force multiplied by the velocity - P=Fv. This is obtained by combining the Work = Force x distance and Power = Work/time formulas.
2.3.10 Define and apply the concept of efficiency
The efficiency of an engine is defined as the ratio between the useful work out and the total work put in. It is also equal to the ratio between the useful power out and the useful power in. This concept can be used not only in engines. Efficiency = WOUT/WIN=POUT/PIN.
2.3.11 Solve problems involving momentum, work, energy and power
Simply combine the formulas in 2.3 to work out whatever is needed. Some tips that may help include simplifying d/t into v whenever useful. Occasionally a question may give you v but the formula you have may have d/t in it. In these cases you can simply replace d/t as v since d/t = v. Whenever giving an answer relating to energy or power, make sure you know whether the question is asking you about the total energy of the useful energy. If the question requires the useful energy, you must multiply the total energy by the efficiency of the engine.
2.4
2.4.1 Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the centre of the circle
For an object to move around in a circle, it must be travelling in a direction at the tangent to the circle where the object is at, and direction of the force being applied must be perpendicular to the direction the object is travelling in. The direction of the force is pointing to the centre of the circle (the radius). The force causing the object to accelerate towards the centre is in the case of a car, the friction, and when an object is whirled around on the air on a string, it is the tention of the string. This force is called the centripetal force. The acceleration caused by this force is called the centripetal acceleration.
2.4.2 Apply the expression for centripetal acceleration
Acceleration = v^2/r
2.4.3 Identify the force producing circular motion in various situations. Examples include the gravitational force acting on the moon and friction acting sideways on the tyres of a car turning a corner
Examples of forces which provide centripetal forces are gravitational forces (planets orbiting in a circle), frictional forces (car driving in circles), magnetic forces or tension (string). F=ma. a = v^2/r. Therefore, F=mv^2/r
| 
