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Unit 6: 1-Dimensional Kinematics

Problem Set D

Overview:

Problem Set D targets your ability to use kinematic equations to analyze the motion of objects.The set consists of 15 problems, 10 of which are routine-style confidence-builders and the remaining five involving complex, mulit-step analyses.

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.

 d = vo • t + 0.5 • a • t2 vf = vo + a • t vf2 = vo2 + 2 • a • d d = (vo + vf) / 2 • t

 where d = displacement t = time a = acceleration vo = original or initial speed vf = 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 problem-solving strategy used in this collection of problems will center around this idea. Each problem consists of a word-story 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.

To be successful on this problem set, you will need to be able to:

• implement a proper problem-solving strategy in which you identify known and unknown (requested) variables using the symbols of the kinematic equations.
• give consideration to units in such a manner that the units will properly cancel when the various performing algebraic operations dictated by the equations.
• diagram a physical situation (on the complex analyses) and use the kinematic equations to generate an equation which expresses the mathematical relationships described by the problem statement.

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.

The Kinematic Equations | Problem-Solving | Sample Problems and Solutions

View Sample Problem Set.

 Problem Description Audio Link 1 Determination of acceleration from vo, vf and d. 2 Referring to the previous problem; determination of the time. 3 Determination of acceleration from vo, vf and t. 4 Referring to the previous problem; determination of the displacement. 5 Determination of time from vo, vf and a. 6 Determination of distance from vo, a and t. 7 Determination of time from vo, vf and d; conversion of units required. 8 Complex analysis involving the determination of acceleration for the second stage of a two-stage motion; conversion of units required. 9 Complex analysis involving the determination of the time required for a trailing hockey player to catch up with the lead hockey player. 10 Referring to the previous problem; determination of the distance traveled during this time. 11 Determination of acceleration from vo, vf and d. 12 Complex analysis involving the determination of the time required for an accelerating car to catch up with a constant speed car. 13 Complex analysis involving the determination of the final separation distance between a trailing car and a lead car; conversion of units required. 14 Complex analysis of a train's motion which decelerates to a rest, waits at the stop and accelerates back up to speed; must determine the time lost in making the stop. Conversion of units required. 15 Determination of the final velocity from vo, t and d.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15

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