Motion in a straight line Kinematics Motion in a straight line

Kinematics The study of how objects move. Three restrictions for now… Straight line only (vertical or horizontal) Objects are treated as points Motion description only (no causes, no forces, no friction, no energy, no air resistance)

Location, Location, Location Position: indication of where an object is based on a frame of reference. Distance: total length of travel. Displacement: change in position of an object. As a general rule these value should be measured in meters (m) and are often represented by the same symbol, d.

They are different! CASE I: Walk from position 0 to position 2 5.0 m 2 1 CASE I: Walk from position 0 to position 2 distance= 10.0 m displacement=10.0 m … but these are the same!

WAIT FOR IT… 5.0 m 2 1 CASE II: Start at position 0, walk to position 2, then return at position 1 distance= 15.o m displacement = 5.0 m

Let’s try again… 5.0 m 2 1 CASE III: Start at position 0, walk to position 2, return to position 0 distance= 20.0 m displacement =0.0 m (No change in position!)

Let’s keep it going… CASE IV: Start at position 2, walk to position 0. 5.0 m 2 1 CASE IV: Start at position 2, walk to position 0. distance= 10.o m displacement = -10.0m (opposite direction of case I) Displacement can indicate the direction of the motion. In general to the right is considered positive and to the left is considered negative.(this is arbitrary)

And going… 5.0 m 2 1 CASE V: Start at position 2, walk to position 0, then return to position 1 distance= 15.0 m displacement =-5.0 m

One more… CASE VI: Start at position 0, return to position 0 5.0 m 2 1 CASE VI: Start at position 0, return to position 0 distance= 20.0 m displacement =0.0 m (No change in position!)

Rate of Motion Speed: distance per unit time s = d/t Velocity: displacement per unit time v = Δd/t= (df – di)/t

The difference… 5.0 m 2 1 Assuming the trip takes 2.0 s, let’s revisit a few cases. CASE I: Walk from position 0 to position 2 distance= 10.0 m displacement=10.0 m velocity = speed = 10.0m/2.0s = 5.0 m/s

Assuming the trip takes 2.0 s, let’s revisit a few cases. 5.0 m 2 1 Assuming the trip takes 2.0 s, let’s revisit a few cases. CASE II: Start at position 0, walk to position 2, then return at position 1 d= 15.o m Δd = 5.0 m speed =15.0 m/2.0s = 7.5 m/s velocity =5.0m/2.0s = 2.5 m/s CASE III: Start at position 0, walk to position 2, return to position 0 d= 20.0 m Δd =0.0 m speed = 20.0m/2.0s = 10.0m/s velocity = 0.0m/2.0s = 0.0 m/s

Assuming the trip takes 2.0 s, let’s revisit a few cases. 5.0 m 2 1 Assuming the trip takes 2.0 s, let’s revisit a few cases. CASE IV: Start at position 2, walk to position 0. d= 10.o m Δd= -10.0m speed = 10.0m/ 2.0s = 5.0m/s velocity = -10.0m/2.0s = -5.0m/s CASE V: Start at position 2, walk to position 0, then return to position 1 d= 15.0 m Δd=-5.0 m speed = 15.0m/2.0s = 7.5 m/s velocity = -5.0 m/2.0s = -2.5 m/s

So direction does matter. Values that only indicate magnitude (amount) are called scalars. Distance, speed, time Values that indicate both magnitude AND direction are called vectors. displacement, velocity