2 1 Reference Point Displacement vs distance You

2. 1 Reference Point (Displacement vs distance) • You choose an origin! • What is displacement vs distance? origin

2. 2 Velocity Average Velocity Units: or *1 m/s = 2. 24 mi /hr

2. 2 Velocity Average Speed Units: or *1 m/s = 2. 24 mi /hr

t Slope = + m/s

The Slope = m/s slope of a p-t graph shows velocity

t Slope = zero m/s

Pos v Neg v If the slope is increasing (+ or-) the quantity will increase : speed ! Pos v Neg v

2. 2 Velocity Instantaneous Velocity 0

It appears we have 2 different average velocities ! Nope. These are 2 separate instantaneous velocities. Slope = + m/s t

2. 4 Acceleration Average Acceleration Units: 2 2 2

v 0 t

t

v 0 t

Speeding Up then Slowing Down v t Slope= m /s 2

Slowing Down then speeding up v t Slope= m /s 2

Very rare to see in AP 1 v t

Substitute y for x if needed Substitute g for a in pure free fall

displacement as function of velocity (I) (II) Substitute (I) and (II) with t X= 1/2 (v+v 0) (v -v 0 / a)

displacement as function of time (I) (II) Substitute (I) and (II) with Vf X= 1/2 (v 0 + at + v 0)t 2

Shaded Area of v-t = displacement 1. The shaded area represent a velocity maintained for a certain time period. 2. If I went 2 m/s for 4 s then I went 8 meters. 3. The area of the graph = 8 m as well ! Why…. start with the units on the axes. . 4. Area= bh Area= (time)(velocity) Area= (s)(m/s)= meter

Shaded Area of v-t = displacement 1. This also calculates negative displacement as well… 2. If I went - 2 m/s from 2 s to 8 s I went - 12 meters. 3. That is due to the fact that I went -2 m/s for exactly 6 seconds 4. Area= b-h Area= (time)(-velocity) Area= (s)(-m/s)= -meter

Shaded Area of v-t = displacement 1. This also works for tringles 2. If I went from 0 m/s to 6 m/s in 4 secs…. . I went 12 meters. 3. That is due to the fact that I went an average of 3 m/s over the 4 second interv 4. Area= ½ bh Area= (time)(velocity) Area= (s)(m/s)= meter

Core Problem 1. 0 A particle is moving in the positive x dimension. Its position at any given time is given by the function: (x) t = 4 t 3 + 3 We will evaluate the particle as It changes through these time periods Dt = 0. 01 s, 0. 2 s, 0. 5 s, and 1. 0 s a) Calculate the particle’s position and fill in the table b) Calculate the particle’s average velocity t actual (s) position (m) Dt (s) v ave (m/s) Work :