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Uniform Acceleration Problems

A MATHEMATICAL MODEL OF MOTION

Chapter 5

 INSTRUCTIONS:  For this homework, you will be  drawing a coordinate axis (in math lingo: “an x-y board”) to solve kinematic (motion) problems.  You MUST draw a coordinate system for each problem that requires you to use one of the kinematic formulas before you plug-n-chug the numbers.  Listed to the right,  are the four kinematic formulas your learned about in chapter 5 and the ones you will need to use to solve the problems below.

Definitions of each of the variables you see above:

v = This is the final velocity (or velocity of impact) (units = m/s)

v0 = This is the initial velocity.  Use a positive (+) value if you initially throw something up.  Use a negative value (-) if you initially throw something down (units = m/s)  If the initial velocity is zero  (v0 = 0), you can remove it from the equation.

a = acceleration.  When  solving problems using gravity, substitute g for a (remember g is a  constant at -9.8 m/s2)  This is because gravity always acts downward.  (units = m/s2)

d = final distance.  In the problems involving objects dropped, etc., d will represent the displacement in the y-direction.  It is positive (+) if the final position is above where you threw it.  It is negative (-) if the final position of the object is below where your threw it. (units = m)

d0 = initial distance.  This is where the object started.  This value is very often = 0 (d0 = 0).  In this case, you can remove it from the equation. (units = m)

t = This the time the object is in motion.  It is always positive.  If you find it to be negative, then you did something wrong!  (units = s)

t0 = This the initial time the object was put in motion.  Yes I know, you do not see this in any of the equations above.  That is because it was assumed in each that t0 = 0, and was therefore eliminated from the equation.  REMEMBER we arrived at each of the equations above from our two favorite equations of average velocity and average acceleration !

Motion Problems:  Remember, when solving the kinematics motion problems, always follow these three steps:

• Always start by writing down everything you know (the variables) and what they are asking you to find out (the unknown variable).  Always show the units!

• The next step is to draw a visual representation of the problem (a picture) to help you keep track of what is happening and what you are looking for. You then need to draw a coordinate system (an x-y board) to determine (+) or (-) values for your variables.

• Now choose which equation fits your problem and plug in the values and solve for your unknown.

 H E Y !   M R .  W I L S O N  Website by Duncan Wilson Page last updated January 07, 2012 The links on this page connect students to resources, which are recommended because of their educational content and value. I do not intend your child to visit any pages beyond those to which I have provided specific links. We recommend that you supervise/monitor your child's Internet activity at all times.