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Physics 218

Lecture 4: Kinematics. Physics 218. Alexei Safonov. Today’s Lecture. Finish up what’s left from last time More math issues Integrals Problem solving techniques Motion in 1-Dimension continued No longer going to use numbers Examples: Stopping a speeding car Free fall

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Physics 218

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  1. Lecture 4: Kinematics Physics 218 Alexei Safonov

  2. Today’s Lecture • Finish up what’s left from last time • More math issues • Integrals • Problem solving techniques • Motion in 1-Dimension continued • No longer going to use numbers • Examples: • Stopping a speeding car • Free fall • Catching a speeder

  3. Checklist for Today • For the rest of this week: • Be ready for the lab (WebAssign) including pre-labs and all • Some sections already had labs this week, but not all • Quiz at the recitation on Chapter 1 • Same here • There was no pre-lecture for today (this week only, this is not typical) • Homework for Chapter 2 is due Sunday on MP • Coming week recitation quiz will be on Chapter 2 • Start Chapter 3 material: • Read the book • Pre-lectures for next week due on Sunday

  4. Acceleration • Acceleration is the “Rate of change of velocity” • Said differently: “How fast is the Velocity changing?” “What is the change in velocity as a function of time?”

  5. Acceleration

  6. Example You have an equation of motion of: X = X0 + V0t + ½at2 where X0, V0 , and a are constants. What is the velocity and the acceleration? V = dx/dt = 0 + V0 + at • Remember that the derivative of a constant is Zero!! Accel = dV/dt =d2x/dt2 =0 + 0 + a

  7. Position, Velocity and Acceleration • All three are related • Velocity is the derivative of position with respect to time • Acceleration is the derivative of velocity with respect to time • Acceleration is the second derivative of position with respect to time • Calculus is REALLY important • Derivatives are something we’ll come back to over and over again

  8. Important Equations of Motion If the acceleration is constant Position, velocity and Acceleration are vectors. More on this in Chap 3

  9. A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt2 - ct3, b= 2.40 m/s2, c = 0.12 m/s3 Calculate: instantaneous velocity of the car at t= 0,5,10 s How long after starting from rest is the car again at rest? Problem with Derivatives

  10. Getting Displacement from Velocity For const acceleration the Equation of motion: X=X0+V0t + ½at2 • If you are given the velocity vs. time graph you can find the total distance traveled from the area under the curve: • X-X0=V0t + ½at2 • Can also find this from integrating…

  11. Definite and Indefinite Integrals

  12. Some Integrals

  13. Our Example with Const. Acceleration

  14. How quickly can you stop a car? You’re driving along a road at some constant speed, V0, and slam on the breaks and slow down with constant deceleration a. • How much time does it take to stop? • How far do you travel before you come to a stop? Where you stop When you hit the brakes

  15. Free Fall • Free fall is a good example for one dimensional problems • Gravity: • Things accelerate towards earth with a constant acceleration • a=g=9.8m/s2 towards the earth • We’ll come back to Gravity a lot!

  16. Throw a Ball up You throw a ball upward into the air with initial velocity V0. Calculate: • The time it takes to reach its highest point (the top). • Distance from your hand to the top • Time to go from your hand and come back to your hand • Velocity when it reaches your hand • Time from leaving your hand to reach some random height h.

  17. Problem • Show that for constant acceleration:

  18. Speeder A speeder passes you (a police officer) sitting by the side of the road and maintains their constant velocity V. You immediately start to move after the speeder from rest with constant acceleration a. • How much time does it take to ram the speeder? • How far do you have to travel to catch the speeder? • What is your final speed? X Police Officer Speeder

  19. Checklist for Today • For the rest of this week: • Be ready for the lab (WebAssign) including pre-labs and all • Some sections already had labs this week, but not all • Quiz at the recitation on Chapter 1 • Same here • There was no pre-lecture for today (this week only, this is not typical) • Homework for Chapter 2 is due Sunday on MP • Coming week recitation quiz will be on Chapter 2 • Start Chapter 3 material: • Read the book • Pre-lectures for next week due on Sunday

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