Kinematics: Velocity and Cart

1.From the data obtained, what is the effect of the height of the track to the cart’s acceleration? The data shows that sinӨ, which is dependent on the height, is getting higher as acceleration is increasing. This implicates that when object is at higher altitude, its acceleration is faster. 2.From the data obtained, how is time, t related to the inclination of the track? Explain why? Time and position of velocity are interrelated to each other and the height and gravitational pull affects the acceleration of a moving and a free falling object. 3.From the data obtained, how would you account the difference between the picket fence’s acceleration and the value of g? The value of the slope of a graph of average velocity versus time will be the acceleration due to gravity of the falling object.

E102-MOTION ALONG A STRAIGHT LINE

PROBLEM:
1.A police car is searching for a fugitive that managed to escape a while ago. Knowing that he is now safe, the fugitive begins to take a rest until he notices a police car approaching him at 10 m/s, accelerating at 5 m/s2 and it is 100 m away. The fugitive grabs a motorcycle and stars it accelerating at the same rate as the police car. How much time will it take the police car to catch the fugitive?

x = xo + vot + 1at2

xpolice = 0m +10m/s (t) + 0.5(5m/s2)t2
xfugitive = 100m +0m/s (t) + 0.5(5m/s2)t2

In order for the police to caught the fugitive, their final
position must be the same. Thus,
xpolice = xfugitive

0m +10m/s (t) + 0.5(5m/s2)t2 = 100m +0m/s (t) + 0.5(5m/s2)t2 (10m/s) t + ( 5 m/s2)t2 = 100m + ( 5 m/s2)t2

t=10 seconds

E102-MOTION ALONG A STRAIGHT LINE

PROBLEM:

2.A car starts from rest and moves along a straight line with an acceleration of a = (3s-1/3) m/s2, where s is in meters. Determine the car’s velocity and position when t = 10s.

A = Vf – Vo

3s-1/3 m/s2 = Vf – 0
10 s

Vf = 30 s-1/3 m/s

X = Xo + vot + 0.5at2
X = 0m + (0m/s) (10s) + 0.5 [(3s-1/3) m/s2][10s]2

X = 150s-1/3 m

E102-MOTION ALONG A STRAIGHT LINE

REMARKS:
The second experiment we did as a group is Experiment 102 Kinematics. Kinematics is the branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it. We have a lot of tools used in this experiment and some examples are dynamic cart, dynamic track, photo gate, smart timer and many more. The cart is in the start line and needs to go the end line, yes the tool are like a straight racetrack. Then we also have tools to record the time it finish the line. We have been in trial and error a couple of times but because of teamwork we actually did it.

CONCLUSION:
Kinematics can help us to know the geometry of motion. Kinematics can help us in our life. For example is that for creating a product, something like that is moving. I therefore conclude that you can determine the average velocity of a dynamic cart and you can determine the acceleration due to gravity using cart’s acceleration. In this process you need to have the things to complete this process; cart, track, a recorder and other tools to record it.

E102-MOTION ALONG A STRAIGHT LINE
INTERPRETATION OF RESULTS

The experiment revolves on the study of motion without considering the forces that causes or develop the motion. It particularly deals with the motion of a particle in a straight line. To determine experimentally the acceleration due to gravity and to study motion by determining the velocity are the primary objectives of this experiment. Time of travel of the cart in a specific displacement was determined using the cart, picket fence and smart timer. Velocity as a function of time is a vector quantity. Both magnitude and direction are required to define it. On the other hand, we often had mistaken identifying speed as tantamount to velocity, which is only its scalar counterpart. The first part uses a cart which is allowed to travel from one end of the track to another in a horizontal path by releasing the button with spring in it. In getting the velocity, the total displacement of the object is divided to time it occupies to reach that certain distance. Velocity is dependent on time and displacement. For every change in displacement, there is also change in time, definitely. Mathematically, in an equation of a line, slope=y/x. By making a position-time graph, we can also determine the velocity using its slope because they are equal. Theoretically, velocity of the cart in the experiment must be constant.

On experimental reasons, it is because, constant force is applied to object to move, and tendency would be to give constant velocity. Aside from this, position-time relation is a linear function, thus it must give a constant slope or constant velocity. Although we made mistake, the data is seemed to be correct since it has small difference from each other. Using its average, its absolute deviation is about 2-3% only. One major source of our error is the differences in the amount of force exerted in pushing/releasing the spring plunger. When we exert great force in pushing it, automatically, the cart will move faster than its original velocity. Aside from this, air resistance contributed the decrease of velocity. In connection with this, one great force that hinders the movement of the track is the air drag.

If the track of motion is inclined at an angle θ, the motion is uniformly accelerated. Acceleration differs from velocity in a way that velocity is the change of position per time of travel on the leveled track which is assumed frictionless while in acceleration, it accounts on the force that pulls it downward which is the gravitational pull of the earth. It makes up its formula a=gsinθ. Because velocity is a vector quantity, acceleration as a function of velocity is also a vector quantity. It is formally defined as the rate of change in velocity over unit of time. On the second part, instead of moving on a horizontal, the cart was allowed to move freely from the upper end to the lower end of the track. Of course, the only force involved here is the gravity, which is pulling the cart to the ground. Every now and then, the altitude of the initial position is changed by interval of 2cm per trial.