Kinematics

Kinematics is the branch of physics that deals with the analysis of the motion of objects

without concern for the forces causing the motion. Scientists have developed

equations that describe the movement of objects within certain parameters, such as

objects moving with a constant velocity or a constant acceleration. Using these

equations, the future position and velocity of an object can be predicted. This

investigation will focus on objects moving with a constant velocity or a constant

acceleration. Data will be collected on these objects, and the motion of the objects

will be analyzed through graphing these data.

Objectives

 Explain linear motion for objects traveling with a constant velocity or constant

acceleration

 Utilize vector quantities such as displacement and acceleration, and scalar

quantities such as distance and speed.

 Analyze graphs that depict the motion of objects moving at a constant velocity

or constant acceleration.

 Use equations of motion to analyze and predict the motion of objects moving at

a constant velocity or constant acceleration.

Time Requirements

Preparation …………………………………………………………………………………5 minutes

Activity 1 …………………………………………………………………………………….15 minutes

Activity 2 …………………………………………………………………………………….20 minutes

Activity 3 …………………………………………………………………………………….20 minutes

Activity 4 …………………………………………………………………………………….10 minutes

Activity 5 …………………………………………………………………………………….20 minutes

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Background

Mechanics is the branch of physics that that studies the motion of objects and the

forces and energies that affect those motions. Classical Mechanics refers to the motion

of objects that are large compared to subatomic particles and slow compared to the

speed of light. The effects of quantum mechanics and relativity are negligible in

classical mechanics. Most objects and forces encountered in daily life can be

described by classical mechanics, such as the motion of a baseball, a train, or even a

bullet or the planets. Engineers and other scientists apply the principles of physics in

many scenarios. Physicists and engineers often collect data about an object and use

graphs of the data to describe the motion of objects.

Kinematics is a specific branch of mechanics that describes the motion of objects

without reference to the forces causing the motion. Examples of kinematics include

describing the motion of a race car moving on a track or an apple falling from a tree,

but only in terms of the object’s position, velocity, acceleration, and time without

describing the force from the engine of the car, the friction between the tires and the

track, or the gravity pulling the apple. For example, it is possible to predict the time it

would take for an object dropped from the roof of a building to fall to the ground using

the following kinematics equation:

= 1

2 2

Where s is the displacement from the starting position at a given time, a is the acceleration of the object, and t is the time after the object is dropped. The equation does not include any variables for the forces acting on the object or the mass or energy

of the object. As long as the some initial conditions are known, such an object’s

position, acceleration, and velocity at a given time, the motion or position of the object

at any future or previous time can be calculated by applying kinematics. This method

has many useful applications. One could calculate the path of a projectile such as a

golf ball or artillery shell, the time or distance for a decelerating object to come to rest,

or the speed an object would be traveling after falling a given distance.

Early scientists such as Galileo Galilee (1564-1642), Isaac Newton (1642-1746) and

Johannes Kepler (1571-1630) studied the motion of objects and developed

mathematical laws to describe and predict their motion. Until the late sixteenth

century, the idea that heavier objects fell faster than lighter objects was widely

accepted. This idea had been proposed by the Greek philosopher Aristotle, who lived

around the third century B.C. Because the idea seemed to be supported by

experience, it was generally accepted. A person watching a feather and a hammer

dropped simultaneously from the same height would certainly observe the hammer

falling faster than the feather. According to legend, Galileo Galilee, an Italian physicist

and mathematician, disproved this idea in a dramatic demonstration by dropping

objects of different mass from the tower of Pisa to demonstrate that they fell at the

same rate. In later experiments, Galileo rolled spheres down inclined planes to slow

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down the motion and get more accurate data. By analyzing the ordinary motion of

objects and graphing the results, it is possible to derive some simple equations that

predict their motion.

To study the motion of objects, a few definitions should be established. A vector refers

to a number with a direction and magnitude (or size). Numbers that have a magnitude

but not a direction are referred to as a scalar. In kinematics, vectors are important,

because the goal is to calculate the location and direction of movement of the object

at any time in the future or past. For example if an object is described as being 100

miles from a given position traveling at a speed of 50 miles per hour, that could mean

the object will reach the position in 2 hours. It could also mean the object could be

located up to 100 miles farther away in 1 hour, or somewhere between 100 and 200

miles away depending on the direction. The quantity speed, which refers to the rate of

change in position of an object, is a scalar quantity because no direction of travel is

defined. The quantity velocity, which refers to both the speed and direction of an

object, is a vector quantity.

Distance, or the amount of space between two objects, is a scalar quantity.

Displacement, which is distance in a given direction, is a vector quantity. If a bus

travels from Washington D.C. to New York City, the distance the bus traveled is

approximately 230 miles. The displacement of the bus is (roughly) 230 miles North-East.

If the bus travels from D.C to New York and back, the distance traveled is roughly 460

miles, but the displacement is zero because the bus begins and ends at the same point.

It is important to define the units of scalar and vector quantities when studying

mechanics. A person giving directions from Washington D.C. to New York might

describe the distance as being approximately 4 hours. This may be close to the actual

travel time, but this does not indicate actual distance.

To illustrate the difference between distance and displacement, consider the following

diagrams in Figures 1-3.

Consider the number line in Figure 1. The displacement from zero represented by the

arrowhead on the number line is -3, indicating both direction and magnitude. The

distance from zero indicated by the point on the number line equals three, which is the

magnitude of the displacement. For motion in one dimension, the + or‒ sign is sufficient

to represent the direction of the vector.