MOTION IN ONE DIMENSION
OVERVIEW
Acceleration is defined as the rate of change of the velocity with time. A freely falling body is an example of a uniformly accelerated motion. A body is said to be freely falling if the lone force acting on it is the pull of the earth or the acceleration of gravity, which is around 9.8 meters per second per second.
Acceleration is defined as the rate of change of the velocity with time. A freely falling body is an example of a uniformly accelerated motion. A body is said to be freely falling if the lone force acting on it is the pull of the earth or the acceleration of gravity, which is around 9.8 meters per second per second.
LEARNING OBJECTIVES:
At the end of this module, you should be able to:1. Understand the relationship between velocity and acceleration through graphical analysis. 2. Solve for height using the concept of freely falling objects.
At the end of this module, you should be able to:1. Understand the relationship between velocity and acceleration through graphical analysis. 2. Solve for height using the concept of freely falling objects.
MOTION IN ONE DIMENSION
Motion in one dimension entails motion along a straight line or in a single direction such as an object moving forward/backward or, alternatively up/down. Some examples of one-dimensional motion include a person driving down a straight road, a kid jogging on a straight track, or a coin being tossed into the air and watching it fall. As previously discussed in LR#1, scalar and vector quantities are used to describe the motion of an object. There are four quantities that are mainly used in evaluating the motion of objects, namely, time, displacement, velocity, and acceleration. Time is a scalar quantity while displacement, velocity, and acceleration are vector quantities.
Motion in one dimension entails motion along a straight line or in a single direction such as an object moving forward/backward or, alternatively up/down. Some examples of one-dimensional motion include a person driving down a straight road, a kid jogging on a straight track, or a coin being tossed into the air and watching it fall. As previously discussed in LR#1, scalar and vector quantities are used to describe the motion of an object. There are four quantities that are mainly used in evaluating the motion of objects, namely, time, displacement, velocity, and acceleration. Time is a scalar quantity while displacement, velocity, and acceleration are vector quantities.
Time is defined as the change or the interval at which the change occurs. After all, it is impossible to know that time has passed unless something changes. Displacement is simply defined as the change in position of an object. Hence, its formula is equal to the final position minus the initial position. Meanwhile, velocity is defined as the rate of change of the object's position with respect to a frame of reference or time. In other words, it is equal to the displacement divided by the elapsed time or simply v = d/t. Consequently, when talking about the rate of change of velocity with respect to time, it is always the acceleration.
KINEMATIC EQUATIONS
Kinematics is the branch of physics that defines the motion of objects with respect to space or time, ignoring the cause of that motion. Kinematic equations are a set of equations that can derive an unknown quantity given that the other quantities are provided. Shown on the left is the four basic kinematic equations. Note that v denotes the final velocity, v0 pertains to the initial velocity, a is the acceleration, t means time, and Δx is the displacement. Some of these kinematic equations will be used in the laboratory experiment such as the number 1 and number 3. Shown below is the laboratory report for the experiment.
Kinematics is the branch of physics that defines the motion of objects with respect to space or time, ignoring the cause of that motion. Kinematic equations are a set of equations that can derive an unknown quantity given that the other quantities are provided. Shown on the left is the four basic kinematic equations. Note that v denotes the final velocity, v0 pertains to the initial velocity, a is the acceleration, t means time, and Δx is the displacement. Some of these kinematic equations will be used in the laboratory experiment such as the number 1 and number 3. Shown below is the laboratory report for the experiment.
Salazar_BSCE2B_LR#3_Motion In One Dimension.pdfThe first part of the experiment is titled "graphical analysis of velocity and acceleration" in which computation is needed to create the two required graphs. For the distance-time graph for constant velocity, the given quantities are time (t) and constant velocity (v). In order to get the distance (d), I used the formula v = d/t and rearranging it to obtain the final formula d = vt. For the distance-time graph for uniform acceleration, I used the kinematic equation number 3 Δx = v0t + ½ at2 and since the initial velocity is zero, the final formula is Δx = ½ at2. Note that this Δx is also the d or distance. The second part of the laboratory experiment is titled "acceleration of motion due to gravity" in which I dropped two objects, a ball and a tape, from the second floor of the CEA building and recorded the time it takes before it reaches the ground. Each object has three trials. Then based on the recorded time and using the gravitational acceleration, I computed for the values of the final velocity just before the object hits the ground and the distance (or height) of the point of release. In computing for the final velocity, I used the number 1 kinematic equation v = v0 + at in which v0 is zero, hence, the final formula is v = at. Moreover, in computing for the distance or height of the point of release, I utilized the number 3 kinematic equation Δx = v0t + ½ at2 and since the initial velocity is zero, the final formula is Δx = ½ at2. Note that in both formulas, t is the time recorded in each trial and a is the gravitational acceleration which is equal to 9.8m/s2. Lastly, I compared the height difference obtained in object A and object B by calculating the percent difference.
Observing the graphs on pages 5 and 6 of the laboratory report, it can be inferred that the distance and time in both graphs have direct or positive relationship in which an increase in time will result to an increase in distance. In other words, as the time increases, the distance of the object covers also increases. The only difference I observed is that the uniform acceleration covers larger distance than with the constant velocity. For instance, at 5 seconds, the distance in the constant velocity is 50 meters while in the uniform acceleration, the distance covered is 125 meters. Also, the first figure shows a straight line while the second figure shows an ascending line with curve. Furthermore, acceleration is the rate of change of velocity. In other words, when velocity changes, acceleration occurs. For instance, an object is said to be accelerating when it is changing its velocity. Meanwhile, the probable reasons for the percent difference of 2.77% obtained in this experiment are mostly personal errors. One would be the inconsistency of the position of the arms holding the object. Error in using the stopwatch is common such as knowing when to stop it as the object lands the ground or maybe the stopwatch already started even if the object is not yet falling. To sum up, the experiment concludes that the acceleration is directly proportional to change in velocity and both acceleration and velocity are inversely proportional to time.
REFLECTION
Motion in one dimension means motion in a single direction such as forward/backward or alternatively up/down. A freely falling object is an example of motion in one dimension. This laboratory experiment made me realize that the definitions of displacement, velocity, and acceleration are somewhat connected to each other. Displacement is defined as the change in position of an object hence its formula is final position minus initial position; velocity is the rate of change in position of an object with respect to time, hence its formula is displacement divided by time; whereas, acceleration is the rate of change of velocity of an object with respect to time, hence its formula is final velocity minus the initial velocity all over the elapsed time. Furthermore, this experiment allowed me to realize the application of the kinematic equations especially in finding the unknown quantities using its formulas provided that the other quantities are given. The distance and time with constant velocity or with uniform acceleration both shows a direct relationship. An increase in time will result to an increase in distance. Also, I have learned that acceleration is directly proportional to change in time and both acceleration and velocity are inversely proportional to time. Moreover, in the concept of freely falling objects is always affected by constant gravitational acceleration which is equal to 9.8m/s2.
Motion in one dimension means motion in a single direction such as forward/backward or alternatively up/down. A freely falling object is an example of motion in one dimension. This laboratory experiment made me realize that the definitions of displacement, velocity, and acceleration are somewhat connected to each other. Displacement is defined as the change in position of an object hence its formula is final position minus initial position; velocity is the rate of change in position of an object with respect to time, hence its formula is displacement divided by time; whereas, acceleration is the rate of change of velocity of an object with respect to time, hence its formula is final velocity minus the initial velocity all over the elapsed time. Furthermore, this experiment allowed me to realize the application of the kinematic equations especially in finding the unknown quantities using its formulas provided that the other quantities are given. The distance and time with constant velocity or with uniform acceleration both shows a direct relationship. An increase in time will result to an increase in distance. Also, I have learned that acceleration is directly proportional to change in time and both acceleration and velocity are inversely proportional to time. Moreover, in the concept of freely falling objects is always affected by constant gravitational acceleration which is equal to 9.8m/s2.
REFERENCES:
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