Kinematics

Classical Mechanics Classical Mechanics: Kinematics: Dynamics: The study of motion related to concepts of force and energy Kinematics: Description of how objects move Dynamics: Study of forces which cause objects to move

Kinematics – Getting Started Translational Motion: Movement without rotation Motion with a reference frame: Motion in reference to a set axis

Kinematics – Getting Started Scalar - Magnitude only, plus a unit Vector - Magnitude and direction, plus a unit Time: t SI Unit (metric): Seconds (s) Elapsed time: Δt Δ Delta (‘change in…’)

Position - Where Where: x, y, or z Change in Position (Δ…) Kinematics Where: x, y, or z Change in Position (Δ…) Displacement - Shortest straight-line distance between two points Vector SI Unit: meters (m) Distance - Entire path taken between two points Scalar SI Unit: meters (m)

How Fast? Rate at which the position changes Average Velocity ( ) Kinematics Rate at which the position changes Average Velocity ( ) displacement time Vector SI Unit: m/s Average Speed distance Average Speed = time Scalar SI Unit: m/s

Problems with Averages Kinematics Averages at times don’t tell the entire story Instantaneous Velocity: velocity measured during an infinitesimally short time interval

Acceleration The rate at which velocity changes Kinematics The rate at which velocity changes Average acceleration ( ) Vector SI Unit: m/s2 Difference between an acceleration of 3 m/s2 and 16 m/s2?

Directions Positive and negative: Kinematics Positive and negative: Tell DIRECTION, not magnitude Which is a larger acceleration? -25 m/s2 or 22 m/s2

Kinematic Equations Condition: a must be constant Assumptions: Kinematics Condition: a must be constant Assumptions: Δt = tf – to = (starting from to of zero) = t xo = starting position (most of the time is also x = 0 m)

Example 1 Kinematics A car goes down a certain road at an average speed of 40 km/h and returns along the same road at an average speed of 60 km/h.  Calculate the average speed in km/h for the round trip.

Example 2 Kinematics A car traveling 88.0 km/h is 110 m behind a truck traveling 75 km/h. How long will it take the car to reach the back of the truck?

Example 3 Kinematics The driver of a car makes an emergency stop by slamming on the car’s brakes and skidding to a stop. How far would the car have skidded if it had been traveling twice as fast initially? (Neglect any reaction time) 4 times as far The same distance 2 times as far The mass of the car must be known