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

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!

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°

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

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

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

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

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

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

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