Unit 6: 1Dimensional Kinematics
Problem Set E
Overview:
Problem Set E targets your ability to use the kinematic equations to analyze physical situations involving motion in one dimensions. Some of the problems involve relatively simple free fall type motion (#19); others involve rather complex analysis which at times include two objects or several stages (#1015). In order to solve these 15 problems, you will have to master the use of the four kinematic equations, understand the characteristics of an object in free fall and practice the habits of an effective problem solver.
The Big Four
Kinematics (the topic of the current unit) is the science of describing the motion of objects. An object's motion can be described using words, diagrams, numbers, graphs and equations. The most commonly used of all equations are the four kinematic equations  affectionately known as the big four. These four equations allow a student to make a prediction of how fast (velocity and speed), how far (displacement and distance) or how much time is required of an object during a motion. The four equations are listed below.






where 
d = displacement 
t = time 

a = acceleration 

v_{o} = original or initial speed 

v_{f} = final speed 
Each of the above kinematic equations have four variables. The usefulness of the equations is that they allow a person to make a prediction about the value of one of the variables if given the value of three other variables. By knowing three, one can calculate a fourth. The problemsolving strategy used in this collection of problems will center around this idea. Each problem consists of a wordstory problem in which information about an object's motion is given. The goal is to carefully read through each story problem to identify at least three pieces of known information in order to calculate a fourth requested piece of information. Often the known information is explicitly stated  "A car moving with an initial velocity of 23.4 m/s...". At other times there are statements included within the word problem such as "Starting from rest, ...? or "...comes to a stop." Such statements imply that the initial velocity is 0 m/s and the final velocity is 0 m/s (respectively).
While the equations are extremely useful, there is one condition which must be met in order for the equations to be used. The object under study must have a constant and uniform acceleration. If an object changes its acceleration at a given point during the motion such that it accelerates at one rate and then later accelerates at a second rate, then the motion must be divided into two phases and each phase must be analyzed separately.
Free Fall
Some of the problems in this set involve free fall type motion. Free fall is a type of motion in which the only force acting upon the moving object is the force of gravity. When an object is in free fall, its motion is influenced solely by the force of gravity and it accelerates at 9.8 m/s/s. The 9.8 m/s/s value is the acceleration of any free falling object irregardless of the characteristics of the object. Such an acceleration is dependent solely upon the gravitational characteristics of the planet and is thus called the acceleration of gravity and represented by the variable g. While the value of g is 9.8 m/s/s on Earth, it is a different value on other planets where the graviational characteristics are different.
There are some unique aspects about the trajectory of a free falling object which are worth noting and serve very useful in one's approach to solving problems. Any object which is originally projected vertically upward and under the sole influenc of gravity will eventually reach a peak height before turning around and falling back downward. At the peak of the trajectory, the velocity of the object is 0 m/s. The time required to reach the peak is equal to the time required to fall from the peak back to its original position. The total time of flight is thus twice the time required to reach the peak. The velocity of the object one second prior to the peak is of the same magnitude as the velocity of the object one second after reaching the peak. And similarly, the velocity of the object two seconds prior to the peak is of the same magnitude as the velocity of the object two seconds after reaching the peak.
To be successful on this problem set, you will need to be able to:
Additional Readings/Study Aids:
The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.
Free Fall  The Acceleration of Gravity  Representing Free Fall by Graphs  How Fast? and How Far?
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