Concept Summary

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Topic | Discussion | Learning Aids
Displacement | 2.1 DISPLACEMENT Displacement is a vector that points from an object’s initial position to its final position. The magnitude of the displacement is the shortest distance between the two positions. 2.2 SPEED AND VELOCITY The average speed of an object is the distance traveled by the object divided by the time required to cover the distance: |
Average speed |

| (2.1)

| The average velocity of an object is the object’s displacement divided by the elapsed time : |
Average velocity |

| (2.2)

| Average velocity is a vector that has the same direction as the displacement. When the elapsed time becomes infinitesimally small, the average velocity becomes equal to the instantaneous velocity , the velocity at an instant of time: |
Instantaneous velocity |

| (2.3)

| 2.3 ACCELERATION The average acceleration is a vector. It equals the change in the velocity divided by the elapsed time , the change in the velocity being the final minus the initial velocity: |
Average acceleration |

| (2.4)

| When becomes infinitesimally small, the average acceleration becomes equal to the instantaneous acceleration : |
Instantaneous acceleration |

| (2.5)

| Acceleration is the rate at which the velocity is changing. |

Use Self-Assessment Test 2.1 to evaluate your understanding of Sections 2.1, 2.2 and 2.3.

| 2.4 EQUATIONS OF KINEMATICS FOR CONSTANT ACCELERATION 2.5 APPLICATIONS OF THE EQUATIONS OF KINEMATICS The equations of kinematics apply when an object moves with a constant acceleration along a straight line. These equations relate the displacement x − x0, the acceleration a, the final velocity v, the initial velocity v0, and the elapsed time t − t0. Assuming that x0 = 0 m at t0 = 0 s, the equations of kinematics are |
Equations of kinematics |

| (2.4)

| (2.7)

| (2.8)

| (2.9)

Use Self-Assessment Test 2.2 to evaluate your understanding of Sections 2.4 and 2.5.

Acceleration due to gravity | 2.6 FREELY FALLING BODIES In free-fall motion, an object experiences negligible air resistance and a constant acceleration due to gravity. All objects at the same location above the earth have the same acceleration due to gravity. The acceleration due to gravity is directed toward the center of the earth and has a magnitude of approximately 9.80 m/s2 near the earth’s surface.
2.7 GRAPHICAL ANALYSIS OF VELOCITY AND ACCELERATION The slope of a plot of position versus time for a moving object gives the object’s velocity. The slope of a plot of velocity versus time gives the object’s acceleration.

Use Self-Assessment Test 2.3 to evaluate your understanding of Sections 2.6 and 2.7.

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