Understanding Linear Motion: Position vs. Time Graphs in Physics

1. Understanding Motion Linear Motion

2. Motion • The motion of an object can only be recognized when something is established as a basis of comparison…a reference point • We say an object is moving when its position changes compared to that reference point • For most day-to-day situations, the Earth, and those things affixed to it, serve as a convenient reference frame that is considered to be stationary.

3. Position and Time • These are the two most fundamental physical quantities that can be measured to describe an object’s motion. • The relationship between these variables can be discovered experimentally and modeled using mathematics in both graphical and equation form.

4. Position vs. Time GraphsThings you should know from the buggy lab… • The magnitude (size) of the slope tells us… • The algebraic sign of the slope tells us… • The magnitude and sign together tell us… • The vertical intercept tells us… • When this graph is a straight line we know…

5. Position vs. Time Graphs The generic equation for a line is… y = mx + b If we replace these generic symbols with ones that represent our motion data, we get… m = v xi Position, x (m) Time, t (s)

6. x = vt + xi • This equation (straight line with slope v and intercept xi) is a model that describes the relationship between position and time for an object moving with constant velocity. x = position of object after time, t v = velocity of object (speed in a direction) t = elapsed time xi = starting position of the object

7. Motion terminology • Distance – how far for an entire sample of motion (only positive) • Position – how far from a reference point in a particular direction (can be negative) • Displacement – Change in an object’s position (x-xi)… how far from the starting point in a particular direction • Speed – distance / time • Velocity – speed in a particular direction