Mathematics in motion - Research Paper Example

P is the momentum of the moving object and m is the mass of the moving object. The mass of the object remains constant. During collision of the vehicle, momentum is conserved. Car collisions are inelastic in nature. A car tries to absorb the impact of collision by diverting the force. During this type of collision momentum is conserved but the kinetic energy is not totally conserved. The transfer of the kinetic energy is difficult. It is easier to determine the position of an object, if the force is known.

The simple way to do this is to double integrate the differential equation of force twice. After the first integration velocity is the yield and after second integration, position of the object can be determined. The method can be utilized to evaluate the trajectory of an object. The method is an easier method that gives an analytical solution to evaluate the position of the object when the force is the function of time (Chemistry.clemson.edu, 1998). The function depicts that the collision between the vehicles is fatal due to the gain in the kinetic energy with respect to the increase in the force with respect to time.

The function gives that force is directly proportional to the displacement. However, it is also dependent on the time. The three equation of motion are: …… (1) …….. (2) ……….. . and the driver accelerates the car with 2m/s2 for 5 second, he will attain a velocity of 11m/s, which is relatively high speed as compared to the initial velocity. In the similar manner if the driver has an initial velocity of 50m/s and driver accelerates the car with 5m/s2 for 10 second, he will attain a velocity of 100m/s that is double the initial velocity.

Thus it is important to take care of the speed laws and accelerate the car recommended manner. In other case, if the driver has the initial velocity of 10m/s and driver accelerates the car with 5m/s2 for 10 second, he will cover about 350 meters. In the similar manner if the car is going too fast consider at 100m/s and we have to stop it to 0m/s in 2 seconds. The car has to decelerate at the rate of 50m/s2. If the rate of deceleration is about 20m/s2, the car would take 5 seconds stop. That speed laws are there to control the speed of the vehicle and stop the vehicle in no time.

The more the car attains speed, the more time it will require to stop the car. In the similar manner, if the car stops in 5 seconds and decelerate at -20m/s2, it will cover about 250 meters to stop the car. If we want to stop the car in just less than 10 meters then the deceleration required will be -500m/s2, which is what we require in case of stopping the car. In this way, speed should be controlled according to the speed laws. References Chemistry.clemson.edu (1998). Newton's Equation of Motion.

[online] Retrieved from: http://chemistry.clemson.edu/chemdocs/marcusgroup/software/CONCEPT/QMA/fma/fma.htm [Accessed: 6 Dec 2013]. Physics.info (2013). Equations of Motion - The Physics Hypertextbook. [online] Retrieved from: http://physics.info/motion-equations/ [Accessed: 6 Dec