1. Warm Up
1. A Child is pushing a shopping cart down an aisle at a speed of m/s. How long will it take this child to push the cart down an aisle with a length of 9.3 meters?
2. A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later. Find the distance that the car travels during braking.
Answers:
s m

2. Vectors
AP Physics 2

3. Definitions Scalar: A quantity with only a magnitude.
Vector: A quantity with a magnitude and direction.
Vector Sum: The sum of two or more vectors.
Vector Component: The projection of a vector along one axis.

4. Scalars and Vectors
Scalar quantities: Temperature, pressure, energy, speed, wavelength, frequency, volume.
Vector quantities: Displacement, acceleration, velocity, magnetic field strength.
(Vectors tell nothing about the path, only the starting and ending points)

5. Vector Notation
𝑐 = 𝑎 + 𝑏 𝑏 𝑎 𝑐

6. Vector Addition rules 𝑏 𝑎 𝑐 𝑑 𝑎 − 𝑎 𝑎 𝑐 𝑑 𝑏 𝑎 + 𝑏 = 𝑏 + 𝑎
( 𝑎 + 𝑏 )+ 𝑐 = 𝑎 +( 𝑏 + 𝑐 ) 𝑏 𝑎 𝑐 𝑑
− 𝑎 𝑎 𝑎 𝑐 𝑑 𝑏

7. Components of Vectors 𝑎= 𝑎 𝑥 2 + 𝑎 𝑦 2 𝑎 𝑎 𝑦 tan𝜃= 𝑎 𝑦 𝑎 𝑥 𝑎 𝑥
Vector Component: The projection of a vector along one axis.
𝑎= 𝑎 𝑥 2 + 𝑎 𝑦 2 𝑎
𝑎 𝑦
𝑎 𝑦 =𝑎 sin𝜃
𝜃= 30⁰
tan𝜃= 𝑎 𝑦 𝑎 𝑥
𝑎 𝑥
𝑎 𝑥 =𝑎 cos𝜃

8. Adding Vectors 𝑏 =7𝑚 𝑎 =5𝑚 𝑐 =?
𝜃 3 =?
𝑐 = 𝑎 + 𝑏
𝑎 =5𝑚, 𝜃 1 =80⁰
𝑏 =7𝑚, 𝜃 2 =75⁰, 𝜃 3 =-15 ⁰
𝑏 =7𝑚
𝜃 2 =75⁰
𝑎 =5𝑚
𝑎 𝑥 =5cos80°=.868𝑚
𝑏 𝑥 =7cos(−15°)=6.761𝑚
𝜃 1 =80⁰
𝑐 =?
𝑎 𝑦 =5sin80°=4.924𝑚
𝑏 𝑦 =7sin −15° =−1.812𝑚
𝑐 𝑥 =.868𝑚+6.761𝑚=7.63𝑚
𝑐 𝑦 =4.924𝑚+ −1.812𝑚 =3.11𝑚
𝑐= 𝑐 𝑥 2 + 𝑐 𝑦 2 = =8.24𝑚
tan𝜃= 𝑐 𝑦 𝑐 𝑥 , 𝜃=tan-1 𝑐 𝑦 𝑐 𝑥 =tan− =22.2°

9. Practice
Chapter 3, Problems 1, 3, 7, 9, 11, 15.