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Chapter 2: Motion in One Direction

Friday, 25-Aug-2006 9:08 AM

Average Speed and Average Velocity
The magnitude of the average velocity is not the average speed. For example, consider the marathon runner discussed here. The magnitude of the average velocity is zero, but the average speed is clearly not zero.

Slopes of Graphs
In any graph of physical data, the slope represents the ratio of the change in the quantity represented on the vertical axis to the change in the quantity represented on the horizontal axis. Remember that a slope has units (unless both axes have the same units). The units of slope in Figure 2.1b and Figure 2.3 are m/s, the units of velocity.

Instantaneous Speed and Instantaneous Velocity
In Pitfall Prevention 2.1, we argued that the magnitude of the average velocity is not the average speed. Notice the difference when discussing instantaneous values. The magnitude of the instantaneous velocity is the instantaneous speed. In an infinitesimal time interval, the magnitude of the displacement is equal to the distance traveled by the particle.

Negative Acceleration
Keep in mind that negative acceleration does not necessarily mean that an object is slowing down. If the acceleration is negative, and the velocity is negative, the object is speeding up!

Deceleration
The word deceleration has the common popular connotation of slowing down. We will not use this word in this text, because it further confuses the definition we have given for negative acceleration.

g and g
Be sure not to confuse the italicized symbol g for free-fall acceleration with the nonitalicized symbol g used as the abbreviation for "gram."

The Sign of g
Keep in mind that g is a positive number - it is tempting to substitute - 9.80 m/s2 for g, but resist the temptation. Downward gravitational acceleration is indicated explicitly by stating the acceleration as ay = - g.

Acceleration at the Top of the Motion
It is a common misconception that the acceleration of a projectile at the top of its trajectory is zero. While the velocity at the top of the motion of an object thrown upward momentarily goes to zero, the acceleration is still that due to gravity at this point. If the velocity and acceleration were both zero, the projectile would stay at the top!