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Home Minds On 1D Kinematics Mission KC3 Speed and Velocity Help Help 7

Mission KC3 Speed and Velocity

The Question

Grandma Henderson challenges Michael Johnson in the 400-meter dash. Grandma H spins her wheelchair wheels five times and gives up 15 meters from the starting line. MJ makes a complete circle around the track and stops at the starting line. In this race, ____.

Define Help

Definition of Speed:
The speed of a moving object refers to how fast the object is moving. It is the distance traveled per unit of time.
 
Definition of Velocity:
The velocity of a moving object is the rate at which the object changes its position.

Think About It

Average velocity calculations are based upon measurements of displacement and time (see Formula Frenzysection). Velocity is a vector quantity and must always account for changes in direction. If a direction change causes an object to begin moving back toward the original position, then the affect of the direction change is to reduce the overall displacement and average velocity. Suppose that a person walks 12 m, east and then 4 m, west in a time of 10 s. The displacement (change in position) of the object is 8 m, east and the average velocity is 0.8 m/s, East. Displacement and velocity must account for the fact that the 4 m segment was in the opposite direction as the 12 m segment. By changing direction and heading back toward the original position, the 4-m segment took away from the overall change in position. Because velocity is the rate of position change, velocity is affected by directional changes.

Minds On Time

If a person does a round-trip motion and finishes at the starting position, then that person does not experience any overall change in position. Overall, the person has not been displaced (that is, not moved out of place) when considering the initial and the final position. While the person may have a large distance of travel (moved over a lot of ground), there is no overall displacement or change in position. As such, the average velocity is 0 for a round-trip motion.

Formula Fix

The average speed of an object can be determined as the ratio of the overall distance traveled per time of travel:
 
ave. speed = distance / time
 
The average velocity of an object can be determined as the ratio of the overall displacement (change in position) per time of travel:
 

ave. velocity = displacement / time

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