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Kinematic Equations for Constant Acceleration

For uniform acceleration there are four equations you should know:

The first equation we have seen before, the modified "distance equals rate times time" when velocity is changing. It should be easy to remember. The second equation is just the definition of acceleration. The third equation was in the last section. The last equation is the only one which is new, obtained by eliminating Δt from equations (7) and (8). It is useful for problems in which the time interval is neither specified nor desired.


A cat drops from a ledge 2 m above the ground. If he accelerates 10 m/s2 downward due to gravity, how much time does it take him to drop?


Let's choose "up" to be positive and DRAW A DIAGRAM (Figure 2-16). We write the quantities we know:


Δy = –2 m


v0 = 0 m/s


a = –10 m/s2


Δt = ?


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Figure 2-16

We look for an equation which involves these quantities and no others. Equation (9) fits, so that





A man drops to his death from the sixth floor of a building (20 m). As he is falling, his acceleration is a constant 10 m/s2 downward. What is his impact velocity? (He was a bad man, and if he had not died many other nice people would have.)


First we DRAW A DIAGRAM (Figure 2-17). The impact velocity is the man's velocity just before he hits the ground v2. Thus our information summary is


v1 = 0 m/s


Δy = –20 m


a = –10 m/s2


v2 = ?


The formula which contains this information and nothing else is (10), so that



His impact velocity is 20 m/s.


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Figure 2-17

In this chapter we looked at the quantities which describe motion, that is, displacement, velocity, and acceleration, and the quantities which affect motion, that is, force and mass. Displacement is a change in location. Velocity is a measure of the change in location per unit time, while acceleration is a measure of the change in velocity per unit time. Displacement, velocity, acceleration, and force are all vectors, that is, they have direction as well as magnitude. We will be dealing with the vector nature of these quantities in future chapters. Most of the mechanics problems on the MCAT involve one dimension and uniform acceleration. In this case we can derive four equations, shown in Section J.
In addition, you should know the equations for the definition of velocity for uniform motion and of average velocity.


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