Chapter 2: Kinematics 2.1 Uniform Motion 2.2 Instantaneous Velocity 2.3 Finding Position from Velocity 2.4 Motion with Constant Acceleration 2.5 Free Fall 2.6 Motion on an Inclined Plane 2.7* Instantaneous Acceleration

Stop to think 2.1 P38 Stop to think 2.2 P44 Stop to think 2.3 P48 Stop to think 2.4 P54 Stop to think 2.5 P61 Example 2.3 P 40 Example 2.4 P 41 Example 2.7 P 45 Example 2.10 P 47 Example 2.14 P 53 Example 2.16 P 56 Example 2.18 P 58

Motion in one dimension Determining the signs of position, velocity and acceleration

Motion along a straight line Can be illustrated by position-versus-time graph: 1 s 2 s 3 s 4 s x Continuous (smooth) curve Origin (x=0) x 10 cm 20 cm 40 cm 70 cm 1 2 3 4 t(s)

Position vs time graphs

Interpreting a position graph 1.What is the position at t =0min 2.What is the position at t =30min 3.What is the velocity at t = 20min 4.What is the velocity at t = 50min 5. What is the acceleration at t=20min 6. If this is V vs. t graph, and x = 0 km at t = 0min. What is the position at t = 80 min

Finding velocity from position graphically

Uniform Motion V(avg)= comstant The position-vs-graph is a straight line Vs = ∆s/ ∆t Sf = Si + Vs ∆t

Instantaneous velocity Using motion diagrams and graphs

Stop to think 2.2 Which velocity-versus-time goes with the position –versus-time graph

Relating a velocity graph to a position graph The value of the velocity at Any time equals the slope of The position graph T

Using calculus to find the velocity Ex. A particle’s position is given by the function 1.What is particle’s position at t = 2s? x = -8+6 = -2 m 2. What is the velocity at t = 2s V|t=2 = -3(2)2+3=-9 m/s

Finding position from Velocity

Example 2.9 1.Where is particle’s turning point? 2.At what time does the particle reach the origin?

Motion with constant acceleration Definition of acceleration If set t0=0s, ∆t = t See page 57

Example 2. 13 A rocket sled accelerates at 50m/s2 for 5. 0 s Example 2.13 A rocket sled accelerates at 50m/s2 for 5.0 s. Coasts for 3.0 s, then deploys a parachute and decelerates at 3.0m/s2 until coming to a halt. What is the maximum velocity of the rocket sled? What is the total distance traveled?

The apple and feather in this photograph are falling in a vacuum Two objects dropped from the same height will, if air resistance can be neglected Hit the ground at the same time and with the same speed

Free Fall g = 9.8m/s2 If we choose the y-axis to point vertically up

Example 2.16 A falling rock A rock is released from rest at the top of 100-m-tall building. How long does the rock take to fall to the ground, what is impact velocity? Y0=100m Y1=0m Vy0= 0 m/s t0 = 0 s

Motion on an inclined plane

Instantaneous Acceleration

Homework 2.50 A 1000Kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16s, then the motor stops. The rocket altitude 20 s after launch is 5100m. You can ignore the air resistance a) What was the rocket’s acceleration during the first 16 s. The rocket launched with Vo = 0, after 16 s b) After motor stops, the acceleration is –g as free fall. c) The rocket’s speed as it passes through a cloud 5100m above the ground

B) Will their separation distance increase, decrease or stay the same Quiz questions: Two stones are release from rest at certain height one after the other A) Will the difference in their speed increase, decrease or stay the same B) Will their separation distance increase, decrease or stay the same