The kinematic equations of motion are derived under the assumption of constant acceleration. While this may at first seem to be a restriction, there are a large number of problems where the acceleration is a constant. The simplest and most obvious are falling body problems, that is, problems involving bodies falling on (or near) the surface of the earth where the acceleration due to gravity is a constant. Falling body problems are taken up in a separate chapter. In the derivation of the kinematic equations of motion a good image to keep in mind is that of falling bodies.

Summarizing, these four kinematic equations of motion are written as

The first three equations relate displacement, velocity, and acceleration in terms of time while the fourth equation does not contain the time.

 Now let's apply these four equations to some typical problems. Remember that the kinematic equations of motion allow us to describe the position, velocity, and acceleration of a mass point.

2-1 A train starts from rest (at position zero) and moves with constant acceleration. On first observation the velocity is 20 m/s and 80 s later the velocity is 60 m/s. At 80 s, calculate the position, average velocity, and the constant acceleration over the interval.

 Solution: Diagram the problem.

Calculate the distance traveled over this 80 s:

The average velocity is

If the acceleration is constant then the average velocity is the average of 20 m/s and 60 m/s, or 40 m/s, and at an average velocity of 40 m/s and 80 s, the distance traveled is 3200 m.

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2-2 For the situation of problem 2-1, calculate the position of the train at 20 s.

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2-3 For the situation of problem 2-1 find the time required for the train to reach 100 m

 Solution:

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2-4 For the situation of problem 2-1 find the velocity of the train at 120 m.