Uniformly Accelerated Motion - Assignment Example

Uniformly Accelerated Motion Acceleration is used in measuring the velo s rate of change. The average acceleration is calculated using the formulae vi is termed as the initial velocity, vf in termed as the final velocity while t is the interval of time where the change occurs. The acceleration units are the velocity over the time taken. Some of the fundamental illustrations are m/s2 and km/h. Acceleration is termed as a vector quantity. This is because it has a direction of final velocity minus the initial velocity. It is therefore, nonetheless to talk of the acceleration magnitude as acceleration only if there is no ambiguity/ When people are concerned with the acceleration tangent to the path travelled, the acceleration direction is known. Therefore, the defining equation is written as (Bueche and Eugene, 74). Uniformly Accelerated Motion Along a Straight Line is regarded as one of the important situation. Here the acceleration vector is a constant and it lied on the displacement vector so that the velocity and acceleration can be defined with a positive and a negative sign. If the displacement is defined by the s, then there will be equation that describes the uniformly accelerated motions as shown below Normally, s is replaced by x or y, and at times and as rewritten as v and vo respectively. Direction is very crucial and a positive direction needs to be selected when the motion along the line is analyzed. Either of the directions needs to be selected as positive. Assuming the acceleration, velocity, and displacement is in the varying direction, and then it is assumed to be negative. The graphical representation for movement along straight line includes plotting distance against time is always regarded as positive. The curve of this graph never reduces take for instance the speedometer and odometer in a vehicle. Since the displacement is termed as the vector quantity, it can be graphed against the period if we confine the motion of a line and then use the positive and the negative signs in specifying the direction. However, it is a conventional practice plotting displacement along straight line against time with the help of a scheme. Such graphical representation along the x-axis may be positive or negative. The graph can either be a plus and get more plus or negative and get more minus. In the two cases, the curve would be a positive slope and the object will be a positive velocity. Additionally, the graph might be positive, have less positive and or a minus, and have more minus. In the two cases, the curve would have a minus slope and the object will be a negative velocity. The instantaneous velocity of any given object at any given time will be the displacement slope against the time graph. Therefore, it can either be +ve, -ve, or even zero. The instantaneous acceleration of the object at a given time will be the gradient of the velocity against the time graph at that given time. For the constant motion and velocity along the x-axis, the x graph against t graph is represented as the titled straight line. For the constant motion and its acceleration, the v against the t graph is represented as a straight line (Bueche and Eugene, 134). In acceleration as a result of gravity, the acceleration of an object moving under the gravitational force is assumed to be g; the gravitational acceleration is directed vertically and downward. On the earth surface, the value differs slightly from one location to the other location. On the moon surface, the average acceleration for the free fall is taken to be 1.6m/s2. In velocity components, supposing that an object moving with a certain velocity at some angle theta from the x-axis as would always is the case with a ball that is thrown into air. The velocity will then have the two-vector component. The corresponding components of the scalar for the velocity will be in addition, and these normally turns out to be always +ve or –ve number depending on the. As a rule of thumb, assuming the velocity is the 1st quadrant,. Additionally, assuming the velocity is in the 2nd quadrant, then . If velocity is found on the 3rd quadrant, then . Finally, when the velocity is found on the 4th quadrant, then . Since the quantities have got signs, and thus implied directions along the axes, it is normal to term them as velocities. The users of this concept will find this important in various texts, but it will not lack the pedagogical drawbacks. Instead, people shall avoid applying velocity on anything but a vector quantity whose direction is precisely stated (Bueche and Eugene, 112). Therefore, for an object that moves with a velocity of 100m/s, the scalar figure of the velocity found on the x-axis will be a negative 100m/s and the speed will always be 100m/s. Using the concept, the projectile problems can easily be solved assuming the friction of the air is ignored. One normally considers motion consisting of independent sections and their vertical motion downward. Based on the dimensional analysis, the mechanical quantities like force and acceleration can be expressed based on their length, mass and its time. For instance, acceleration is defined by length divided by the time taken. The dimension of volume is , while that of the velocity is . Since force is multiplied by the rate of acceleration, their dimensions are . The dimensions are important in checking the equations since every equation term must have similar dimensions. For instance, the equation dimensions will be Therefore, every element has the length dimension. One needs to take note that the equations have similar dimensions. For instance, an equation can never have volumes added to the force or to an area minus the velocity. These terms do not have similar dimensions. In conclusion, the acceleration units are the velocity over the time taken. Some of the fundamental illustrations are m/s2 and km/h (Bueche and Eugene, 74). Reference Bueche, F., and Eugene Hecht. Schaums outline of theory and problems of college physics. 9th ed. New York: McGraw-Hill, 1997. Print. Read More