# Conceptual Physics – Chapter 4:Linear Motion

An object is moving if
It’s position relative to a fixed point is changing.

Speed
distance ÷ time

Average Speed
Total distance covered ÷ Time Interval

Instantaneous Speed
The speed at any instant

Units of Speed
km/h, mi/h, m/s

Velocity
speed in a given direction

Constant velocity
motion in a straight line at constant speed

Changing velocity
change in either the speed or the direction or both

Acceleration
Change of velocity ÷ Time Interval

Deceleration
decreases in speed

Change in direction
Results in a form acceleration

Change in speed (along a straight line)
Results in an acceleration defined by (change in speed) ÷ time interval

Free fall
An object moving under the influence of gravitational force only

Elapsed time
The time that has elapsed since the beginning of any motion.

Acceleration of an object in free fall
∼10 m/s² (or more closely 9.8 m/s²)

instantaneous speed ν of an object falling from rest
ν=gt where g is acceleration due to gravity and t is the elapsed time from the resting position

instantaneous speed of and object thrown straight up in the air
ν= ν₁-gt where ν₁ is the initial upward velocity, g is acceleration due to gravity and t is the elapsed time from the beginning of the throw

distance an object travels in free fall from rest
d=½gt² where g is acceleration due to gravity and t is elapsed time from the resting position

What does the speed versus time graph look like for a free falling object?
It is a straight line or linear because the acceleration is constant. The slope of the line represents the acceleration due to gravity.

What does the distance versus time graph look like for a free falling object?
It is parabolic or nonlinear because the speed is increasing at the rate of the square of time elapsed (it is exponential). The slope of the line at a particular point represents the speed at that particular instant in time.

How does air resistance affect falling objects?
Air resistance noticeably slows the motion of things with large surface areas like falling feathers or pieces of paper. But air resistance less noticeably affects the motion of more compact objects like stones and baseballs.

What is the relationship between velocity and acceleration?
Acceleration is the rate at which velocity itself changes.