# Equations of Motion – Research Proposal Example

The paper "Equations of Motion" is a wonderful example of a research proposal on physics. Various components of a moving object can be described by the use of equations of motion. The kinematic principles such as velocity, displacement, acceleration, and time can also be derived from the same equations. From the fundamental laws of constant acceleration, their equations are normally referred. These laws are applied in situations where acceleration is constant, and the motion of the object is in a straight line. The three equations of motion are: (a) (b); and, (c) s = Where; a = acceleration (m/s²) t = time (s) u = initial velocity (m/s) v = final velocity (m/s) s = displacement (m) From the equations, the first one is based on a velocity-time relationship, In other words, when acceleration is constant, the rate of change of velocity is constant.

If acceleration occurs for long, then the change of velocity will be greater (William, 2009). Also, when acceleration is constant, the rate at which velocity is changing becomes directly proportional to time but if the object is not accelerating, the initial and final velocities will be equal. In the second equation, it is based on the relationship between displacement and velocity.

If the initial velocity is equal to zero, then the acceleration gets constant, and as a result, displacement is equated to the square of velocity. In the third equation, the relationship between time and displacement is highlighted. A change in object displacement is directly proportional to time squared if the initial velocity is zero and acceleration is constant. The same equations of motion also apply to a projectile. In case of projectile, there are two forces that act on an object, which are the force of air resistance and gravity.

Gravitational force influences vertical velocity. It has a constant value of 9.81 m/s2. Further, the horizontal velocity of a projectile is influenced by air resistance (Thomas & Sherwood, 1972). At times it is ignored because its value is negligible. If a projectile object is released and then lands at the same height, then it implies that both its initial and final velocities are equal. Also, the time taken to reach the top or apex is equated to half of the total time for the motion.

That is, Peak height = ½ t if both the initial and final velocities are the same. In finding the peak height, we take the final velocity to be zero (Niels & Mads, 1996). In other words, a projectile changes direction when velocity becomes zero. Also, if we drop an object from a given height, we take the initial velocity to be zero. Objectives The objectives of this report are: To validate and demonstrate the applications of the equations of motion To use the equations of motion in calculating time, acceleration, velocity, and displacement Theory The equations of motions are simple mathematical formulas used to describe the acceleration or velocity of a body in relation to some frame of reference.

In classical mechanics, the fundamental equation of motion is F = ma (Lindberg & Florence, 1987). This is obtained from the second law of Newton where force acting on a body is equated to mass multiplied by acceleration (American Institute of Physics, 2005).