Summary for Chapter 3: Motion

This chapter explains how we describe the motion of objects and there are 3 important ideas in the chapter.

1. Position. We measure the position of an object by giving its position relative to some reference point. The position is the distance and direction from the reference point.
   

A related concept is the change in position. The is the difference between the final position and the initial position, i.e.

Change in Position = Final Position – Initial Position


2. Velocity. The velocity is the rate at which the position is changing, i.e. how fast the position is changing. The average velocity is defined as



The velocity has a magnitude and a direction and it is a vector. It has units of distance divided by time, e.g. m/s. As the change in time becomes small, this becomes the instantaneous velocity. Note that the time interval is the interval corresponding to the change in position. It is a measure of how many meters the object moves per second.

3. Acceleration. This is the rate of change of velocity and the average acceleration is defined as
   

The acceleration has a magnitude and a direction and it is a vector. It has units of velocity divided by time or m/s². It measures how much the velocity changes per second.

Note that an object moving with a constant velocity has no change in its velocity so its acceleration is 0.  

4. Speed. The speed of an object is the magnitude of the instantaneous velocity. It does not have a direction associated with it and is not a vector. The average speed is

An object moving with a constant speed will have a non-zero acceleration if the direction of its motion changes.

• If an object moves from x = 3m to x = 7m in 3s, its average velocity is 4m/3s = 1.3 m/s. The positive velocity indicates it is moving in the positive x direction.

• If the change were from 7m to 2m in 2s, the velocity would be –5m/2s = -2.5 m/s. The – indicates it is moving the negative direction.
• If and object is moving with a constant velocity of 2m/s, how far will it move in 3s? Here you note that the change in position is the (velocity) x (time interval), or (3s) x (2m/s) = 6m.
• If the velocity is constant the acceleration is 0 because the change in velocity is 0.
• If the acceleration is +3m/s², how much will the velocity change in 5s? The change in velocity = (acceleration) x (time interval) = (5s) x (3m/s²) = 15 m/s.

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