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Chapter 2

Chapter 2. Motion in One Dimension. What is Mechanics. The study of how and why objects move is called Mechanics. Mechanics is customarily divided into 2 parts kinematics and dynamics .

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Chapter 2

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

  2. 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

  3. 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

  4. Describing MotionThree 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

  5. 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

  6. 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

  7. Describing Instantaneous VelocityThree 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

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