Motion in One Dimension Chapter 2 Motion in One Dimension Herriman High AP Physics C

Herriman High AP Physics C What is Mechanics The study of how and why objects move is called Mechanics. Mechanics is customarily divided into 2 parts kinematics and dynamics. We will begin with the simplest part of kinematics – motion in a straight line. This is know as linear or translational motion. Herriman High AP Physics C

Descriptions of Motion All motions are described in terms of a position function – X(t) Motions can be described both graphically and mathematically and we will use both descriptions in describing motion in physics Herriman High AP Physics C

Describing Motion Three Common Situations No motion X(t) = A Motion at a constant speed X(t) = A + Bt Accelerating Motion X(t) = A + Bt + Ct2 Herriman High AP Physics C

Average Velocity If you divide distance by time you get average speed Example: S = D/t = 500 miles/2 hours =250 mph If you divide displacement by time you get average velocity Example: Vavg = Δx/Δt = 500 miles North/2 hours = 250 mph North Herriman High AP Physics C

Instantaneous Velocity Unlike average velocity which takes a mean value over a period of time, instantaneous velocity is the velocity function at a given instant, this is a derivative of the position function V(t) = dx/dt Herriman High AP Physics C

Describing Instantaneous Velocity Three Common Situations No motion X(t) = A X = 5 m V(t) = dx/dt = 0 m/s Motion at a constant speed X(t) = A + Bt = 5 + 3t V(t) = dx/dt = 3 m/s Accelerating Motion X(t) = A + Bt + Ct2 = 5 + 3t + 4t2 V(t) = dx/dt = 3 + 4t m/s Herriman High AP Physics C

Herriman High AP Physics C Average Acceleration Acceleration is defined as the change in velocity with respect to time a = Δv/t = (v2 – v1)/t Δ – the greek symbol delta represents change Example: If a car is traveling at 10 m/s and speeds up to 20 m/s in 2 seconds, acceleration is: a = (20 m/s – 10 m/s)/2 seconds = 5 m/s2 Herriman High AP Physics C

Describing Instantaneous Acceleration Motion at a constant speed V(t) = 3 m/s A(t) = dv/dt = 0 m/s2 Accelerating Motion V(t) = 3 + 4t m/s A(t) = dv/dt = 4 m/s2 This is motion with a constant acceleration the most common case we will cover during this course Herriman High AP Physics C

Herriman High AP Physics C Important Variables x – displacement – measured in meters v0 (Vnaught) – Initial Velocity – in m/s vf (Vfinal) – Final Velocity – in m/s a – acceleration – in m/s2 t – time – in seconds Herriman High AP Physics C

Motion with Constant Acceleration Since a = (vf – v0)/t we can rearrange this to: vf = v0 + at and since x = vavgt and since vavg = (vf + v0)/2 A new equation is derrived: x = v0t + ½ at2 Herriman High AP Physics C

Motion with Constant Acceleration Using this equation: x = v0t + ½ at2 and since we can rearrange a previous equation: vf = v0 + at to solve for time which gives us: t = (vf – v0)/a Substituting the second into the first we get: vf2 = v02 + 2ax Herriman High AP Physics C

Summary of the Kinematic Equations Just a hint – Your “A” truly depends upon memorizing these and knowing how to use them! Vavg = x/t vavg = (vf + v0)/2 vf = v0 + at x = v0t + ½ at2 vf2 = v02 + 2ax Herriman High AP Physics C

Problems Using the Kinematics Acceleration of Cars Braking distances Falling Objects Thrown Objects Math Review – The Quadratic Equation x = (-b± SQRT(b2-4ac))/2a Herriman High AP Physics C