Problem 1 - Earth fixed is a geographic  coordinate system and Cartesian coordinate system, and is sometimes known as a "conventional terrestrial" system. It represents positions as an X, Y, and Z coordinate. The point (0,0,0) is defined as the center of mass of the Earth. The Earth coordinate system rotates with the earth around its spin axis. As such, a fixed point on the earth surface has a fixed set of coordinates.

Body fixed is a non inertial body coordinate system and is fixed in both origin and orientation to the moving craft. The craft is assumed to be rigid. The orientation of the body coordinate axes is fixed in the shape of body.

Body fixed coordinate system is used to study rotational excitation in full collision. Whereas earth fixed coordinate system is useful for positioning geo-stationary objects such as satellites.

Problem 2 - Steps for solving a dynamics problem

1- Draw a picture of the problem, if you don't already have one.

2- Draw a free-body diagram for each object of interest, showing all forces that act on that object. You may need to define new variables for forces that are not known.

3- Determine what you know about the acceleration of each object.

4- Choose a coordinate system in which to analyze each object.

5- Write Newton's 2nd Law for each object, filling in the forces and accelerations from your free-body diagram.

6- Write down additional constraint equations based on any other knowledge you have about the problem that hasn't yet been captured in an equation.

7- Solve the resulting system of "n" equations, "n" unknowns

Problem 3 - SAE convention of coordinate system: The society of automotive engineers has established the SAW vehicle coordinate system. This is the system that is used for body fixed coordinates. This coordinate system defines the longitudinal axis of vehicle as x, the lateral axis as y, and the vertical axis as z, the points towards the ground.

Problem 4 - Alembert's principle, alternative form of Newton's second law of motion, stated by the 18th-century French polymath Jean le Rond d'Alembert. In effect, the principle reduces a problem in dynamics to a problem in statics. The second law states that the force F acting on a body is equal to the product of the mass m and acceleration a of the body, or F = ma; in d'Alembert's form, the force F plus the negative of the mass m times acceleration a of the body is equal to zero: F - ma = 0. In other words, the body is in equilibrium under the action of the real force F and the fictitious force -ma. The fictitious force is also called an inertial force and a reversed effective force.

Problem 5 - In power limited acceleration; the vehicle reaches its peak acceleration because the engine cannot deliver any more power. Intraction limited acceleration, the engine can and does deliver more power, but vehicle acceleration is limited because the tires cannot transmit any more driving force to the ground.

The passenger car has traction acceleration which prevents skidding while accelerating so the car can quickly escape a dangerous situation.

Problem 6 - When decelerating, the weight and energy transfers to the front of the vehicle and as a result front brakes are larger since they have more energy to cope with, and that extra weight also gives the front wheels extra grip and thus more braking ability.

Rear wheel drive car spreads the weight of its drive train more evenly front-to-rear. This is why most sports cars and virtually all race cars are RWD.

Problem 7 - With a locked differential, both rear wheels will always turn at exactly the same rate, and power is always distributed 50-50. This is great for accelerating out of corners, but not so great for things like tight corners, because the inside and outside rear wheels are making different arcs around the turn, and will naturally turn at different rates. For this reason, no street car ever comes with a locked diff.

With a totally open differential, each rear wheel operates totally independently. If the car was stationary, the left wheel on pavement and the right wheel on sheet ice with no traction, applying the throttle would send all the engine's power to the wheel on the ice, and the car wouldn't move. When cornering on the track, the inside rear wheel is un-weighted as the weight all shifts to the outside. When you accelerate out of the corner, a car with an open diff is going to send more power to the wrong place -- the wheel without the traction. As a result, you're not going to be able to rotate the car as well, and put down as much power on corner exit.

Problem 8 - Over the course of drive, as a result of alternating between braking and acceleration and of course steering, tires get heated up. When this happens, the air within the tires gets heated up, causing the air within the tire to expand. This expanding air exerts force on the tire from inside thus increasing tire pressure.

The following figure shows the pressure regions on a car:

Problem 9 - Vehicle dynamics refers to the dynamics of vehicles is a part of engineering primarily based on classical mechanics vehicle dynamics is the motion of the vehicle generated by the steering action, through which the vehicle is capable of independent motion.

The dynamic behavior of vehicles can be analyzed in several different ways. This can be as straightforward as a simple spring mass system, through a three-degree of freedom (DoF) bicycle model, to a large degree of complexity using a multi body system simulation.

The vehicle is represented as a rigid body projected to the ground. In describing the motion of the rigid body, the definition of a reference coordinate frame is necessary. Depending on particular body motion characteristics, there could be many ways of defining the coordinates for describing the body motion.

Problem 10 - Elements of brake system:

1. Brake Pedal

2. Brake Booster

3. Master Cylinder

4. Brake Fluid

5. Hydraulic Lines

6. Proportional Valve

7. Hydraulic Calipers

8. Disc Brakes

9. Brake Pads

10. Rotor

11. Drum Brakes

12. Drum

13. Brake Shoes

14. Wheel Cylinder

15. Antilock Braking System (ABS)

16. Electronic Wheel Sensors

17. Emergency Brake

In disc brake (usually located at the front of the vehicle), the brake fluid is pumped through a hydraulic line toward the hydraulic caliper. The caliper is fitted with a pair of fiber brake pads that grab a spinning metal disk - called rotor- attached to the front axle in order to slow down the vehicle. The pads being always in contact with the rotor, they need to be periodically checked and adjusted to detect any sign of wear.

A drum brake (usually located at the rear of the vehicle) consists of a rotating drum that is attached to the wheel, and two expanding brake shoes. The brake shoes are curved metal pads equipped with a fiber brake lining around their outer arc; they are attached to a non-rotating part of the system.  When brake pressure is applied, the brake fluid flows through a hydraulic line toward the wheel cylinder located between the brake shoes. The wheel cylinder then expands the shoes outward toward the inside of the drum. This creates friction slowing the rotating part of the drum and consequently the wheel.

Working principle of friction based brakes:

Friction brakes commonly use friction between two surfaces pressed together to convert the kinetic energy of the moving object into heat, though other methods of energy conversion may be employed. For example, regenerative braking converts much of the energy to electrical energy, which may be stored for later use. Friction brakes on automobiles store braking heat in the drum brake or disc brake while braking then conduct it to the air gradually. When traveling downhill some vehicles can use their engines to brake.