# Kinematics The study of motion in One Dimension Kinematics The study of motion in One Dimension Unit 2 Motion Relative motion Quantifying Motion Scalar vs. Vector Speed vs. Velocity Distance vs. Displacement Acceleration Kinematic equations

Graphical interpretation of motion Free fall motion Classification of Physics Quantities Vector - quantity with both magnitude (size) and direction Scalar - quantity with magnitude only Vectors: Displacement Velocity Acceleration

Momentum Force Scalars: Distance Speed Time Mass Energy Sign Conventions Positive sign Travel East, to the

right or travel North, upwards Negative sign Travel West, to the left or travel South, downwards Units Units are not the same as quantities! Quantity . . . Unit (symbol) Displacement & Distance . . . meter (m) Time . . . second (s)

Velocity & Speed . . . (m/s) Acceleration . . . (m/s2) Mass . . . kilogram (kg) Momentum . . . (kg m/s) Force . . .Newton (N) Energy . . . Joule (J) Kinematics definitions Kinematics branch of physics; study of motion Distance (d ) how far you have traveled, regardless of direction (length of the path traveled)

Displacement (d) where you are in relation to where you started, includes direction (length and direction from start to finish) Distance vs. Displacement You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (green arrow). What if you drove in a circle? start stop

Speed, Velocity, & Acceleration Speed (v) how fast you go Velocity (v) how fast and which way; the rate at which displacement changes Acceleration (a) how fast you speed up, slow down, or change direction; the rate at which velocity changes Speed vs. Velocity Speed is a scalar (it does not consider direction) Ex: v = 20 mph

Speed is often the magnitude of velocity. Velocity is a vector (it considers both speed and direction). Ex: v = 20 mph at 15 south of west Velocity & Acceleration Sign Chart VELOCITY A C C E L E R

A T I O N + - + Moving forward;

Moving backward; Speeding up Slowing down - Moving forward; Moving backward;

Slowing down Speeding up Kinematics Formula Summary For 1-D motion with constant acceleration: vf = v i + a t v = (vi + vf ) / 2 av g d = vi t + a t 2

1 vf = v + 2 a d 2 2 2 i a = v/t v = d/t ProblemSolving

Method Vi Vf V Vbar a x

t Graphing Motion Types of Motion Graphs d-t displacement vs. time v-t velocity vs. time a-t acceleration vs. time d-t Graph with Constant Speed The slope of a distance-time graph represents velocity. A constant slope means a constant

velocity. The slope can be positive, negative , or zero. Distance-Time Graph Distance Positive Slope= Positive Velocity Zero Slope = Zero Velocity Negative Slope=

Negative Velocity Time d-t Graph with Changing Velocity 120 100 80 Distance This curve shows a changing slope which

means a changing velocity 60 40 20 0 -20 0 2

4 6 Time 8 10 12 Finding the Velocity

120 100 Distance 80 60 40 20 0 -20 0

2 4 6 Time 8 10 12

The slope of the tangent line to the curve represents the instantaneous velocity F D E

B A C Which one(s) are motionless? Which one(s) have a constant velocity? Which one(s) are accelerating? Which one(s) return to their starting position? Which one(s) have a positive

velocity? Which one(s) meet? v-t Graph with Constant Acceleration The slope of a speed time graph represents acceleration. A constant slope implies a constant acceleration. The slope can be positive, negative, or zero Velocity-Time Graph

Velocity Positive Slope= Positive Acceleration Zero Slope = Zero Acceleration Negative Slope= Negative Acceleration Time v-t Graph Displacements The area under the curve to the taxis represents the displacement of the

object. The area can be found using simple geometry formulas. The area may be negative if the curve lies under the t-axis. Velocity v-t Graph Displacements Area = Length x Width Displacement Time

v-t Graph Displacements Velocity Area = 1/2 Base x Height Disp. Time Speed of a car v. time Which one(s) are motionless?

Which one(s) have a constant velocity? Which one(s) change their motion? Which one(s) have a positive velocity? Which one(s) are accelerating? Which one(s) displace the least? a-t Graph with Constant Acceleration The slope of an acceleration-time

graph will be zero in this course. A zero slope implies a constant acceleration. The area under the curve represents the change in velocity of the object. Acceleration a-t Graph Change in Velocities Area = Length x Width v Time

Summary d-t Graph Slope represents velocity v-t Graph Slope represents acceleration Area under curve represents displacement a-t Graph Area under curve represents v