1. Motion in 1D, Vectors and Velocity
Unit 2: Kinematics I
Motion in 1D, Vectors and Velocity

2. Describing Motion
Kinematics describes quantitatively how an object moves through space.
(rigid and non-rotating, motion is based on the center of the object)
Dynamics focuses on change in motion(e.g. forces etc.) We will get to this later!

3. Vectors
A Vector is a quantity that has both a magnitude and a direction.
Think of an arrow (It has a length and it points in a certain direction)
Magnitude: The strength or length of the vector (scalar part)
Direction: North, South, East, West etc. (Mostly given in degrees or radians)
𝒙 =𝟏𝟎𝒎
𝟑𝟕°

4. Vector Displacement Velocity Acceleration Magnitude (Scalar) Direction
Distance
(20m)
(East)
Velocity
Speed
(17.8 m/s)
(45⁰)
Acceleration
(9.8 m/s2)
(down)

5. Types of Vectors Displacement: How far I’m moving.
Velocity: How fast I’m moving.
Acceleration: How fast my velocity is changing.
Stepping on the gas pedal to drive faster
Hitting the breaks to slow down

6. To study motion we need a frame of reference
It tells us where the zero position is
It tells us which way is the positive direction
Example: Moving car starts at position x = 0 at time t = 0 and moves in positive direction x
t = 0
t = 10 s

7. Displacement Displacement is a change in position x = xf  xi
displacement = final position  initial position
“” means “change in” xi xf x

8. Displacement can be positive or negative
Displacement is not always equal to the total distance traveled
If a cat walks 10 m to the right, and then 7 m back to the left
Total Distance traveled = ______
Total Displacement = ______
17 m
3 m x
negative displacement

9. Velocity is the time rate of change of position
Average velocity is defined as a change in position divided by a change in time:
𝑽 𝒂𝒗𝒈 = ∆𝒙 ∆𝒕 = 𝒙 𝒇 − 𝒙 𝒊 𝒕 𝒇 − 𝒕 𝒊
t is the time interval of the motion
As we can see average velocity is just displacement over the corresponding time interval

10. Velocity vs Speed Velocity is not the same as speed
Velocity has magnitude and direction
Speed has only magnitude and is always a positive number
Graphically, velocity is the slope of the position-time graph
slope = rise/run
Instantaneous velocity is the velocity of an object at an instant in time (one point)
Graphically, we find the tangent line at that point and calculate the slope