2. Physics 221 Chapter 2

3. Speed Speed = Distance / Time v = d/t

4. Problem 1... Average Speed You drive from city A to city B(50 miles) at an average speed of 50 m.p.h. and from city B to city C (140 miles) at an average speed of 70 m.p.h. What is your average speed? A. 50 m.p.h. B. 60 m.p.h. C. 63.3 m.p.h. D. 70 m.p.h

5. Solution 1... Average Speed You drive from city A to city B(50 miles) at an average speed of 50 m.p.h. and from city B to city C (140 miles) at an average speed of 70 m.p.h. What is your average speed? A. 50 m.p.h. B. 60 m.p.h. C. 63.3 m.p.h. D. 70 m.p.h

6. Speed and Velocity Velocity is speed in a specified direction Car A going at 30 m.p.h. EAST and car B going at 30 m.p.h. NORTH have the same speed but different velocities! A car going around a circular track at 30 m.p.h. has a CONSTANT SPEED but its VELOCITY is CHANGING!

7. Problem 2... Speed and Velocity John Denver negotiates his rusty (but trusty) truck around a bend in a country road in West Virginia. A. His speed is constant but his velocity is changing B. His velocity is constant but his speed is changing C. Both his speed and velocity are changing D. His velocity is definitely changing but his speed may or may not be changing

8. Solution 2... Speed and Velocity John Denver negotiates his rusty (but trusty) truck around a bend in a country road in West Virginia. A. His speed is constant but his velocity is changing B. His velocity is constant but his speed is changing C. Both his speed and velocity are changing D. His velocity is definitely changing but his speed may or may not be changing

9. Instantaneous Velocity Instantaneous means measured at a given instant or moment (“Kodak moment”). Experimentally, this is virtually impossible. One must measure the distance over an extremely short time interval Average means measured over an extended time interval. This is easier to measure.

10. Distance and Displacement Displacement measures how far an object is from the starting point. Distance and Displacement can be very different if the object does not proceed in the same direction in a straight line!

11. Problem 3... On the road again! A car travels East from point A to point B (3 miles) and then North from point B to point C (4 miles). (a) What distance did the car travel? (b) What is the car’s displacement? AB C

12. Solution 3... On the road again! A car travels East from point A to point B (3 miles) and then North from point B to point C (4 miles). (a) Distance traveled is 7 miles (b) Displacement is 5 miles(NE?) AB C

13. Speed and Velocity... revisited! Speed = distance / time Velocity = displacement / time For translational motion (straight line) in the same direction, speed equals velocity! Remember to specify the magnitude and the direction for displacement and velocity. These are VECTOR quantities

14. x = 3 t 2 The position of a particle moving along a straight line is given by the equation x = 3 t 2 A. What is the position of the particle when t = 5 s ? B. What is the speed of the particle when t = 5 s?

15. x = 3 t 2 A. the position of the particle when t = 5 s is 75 m B. The speed of the particle is: v = dx/dt v = 6 t v = 30 m/s Note: Average speed is 15 m/s but instantaneous speed at t=5s is 30 m/s

16. Acceleration Acceleration is the rate of change of velocity a = ( v f - v i ) / t

17. Problem 4... Translational Motion Q. Is the speed constant at t=10s? Q. When is the acceleration zero? Q. When is it slowing down (decelerating)? Q. What is the acceleration at t=7s?

18. Solution 4... Translational Motion Q. Is the speed constant at t=10s? N0! Q. When is the acceleration zero?15s, 20s, etc. Q. When is it slowing down (decelerating)?45s,50s etc. Q. What is the acceleration at t=7s? 1 m/s 2

19. Problem 5... Car on a straight road time The speed at t=0 s is v i =0 At t=6 s, v f = 18 m/s (a) Calculate d (b) Calculate a and v at 4s speed

20. Solution 5a Distance = Area under v vs. t graph Area of a rectangle = base x height Area of a triangle = 1/2 x base x height d = 1/2 x (V f - V i ) x t d = 54 m

21. Solution 5b a = (V f - V i ) / t a = 3 m/s 2 V f = V i + a t V f = 0 + 3x4 V f at 4s = 12 m/s

22. Problem 6 Car accelerating on a straight road Given V i = 2 m/s and a = 3 m/s/s Calculate V f when t= 8s Draw the speed vs. time graph Calculate d when t = 8s

23. Solution 6 V f = V i + a t V f = 26 m/s d = Area = rectangle + triangle d = V i t + 1/2 a t 2 d = (2)(8) + 1/2 (3) (64) d = 112 m speed time

24. Equation Summary for uniform acceleration (No Jerks Pleeeease!) V f = V i + a t d = V i t + 1/2 a t 2 V f 2 = V i 2 + 2ad V ave = (V f + V i ) / 2

25. Problem 7 A car accelerates from a stop light and attains a speed of 24 m/s after traveling a distance of 72 m. What is the acceleration of the car?

26. Solution 7 The equation that comes to our rescue is: V f 2 = V i 2 + 2ad (24 ) 2 = (0) 2 + 2a(72) a = 4 m/s 2

27. Problem 8... Free Fall Acceleration due to gravity is 9.8 m/s 2 (sea level on Earth) (a) A cat falls off a ledge. How fast is it moving 3 seconds after the fall? (b) What is the distance traveled by the unfortunate cat?

28. Solution 8... Free fall V f = V i + a t (a) V f = 0 + (9.8)(3) V f = 29.4 m/s (b) d = V i t + 1/2 a t 2 d = 0 + (1/2)(9.8)(9) d = 44.1 m

29. Problem 9... Apple tree Big apple is twice as big as Little apple. Both fall from the same height at the same time. Which statement is correct? A. Big and Little reach the ground at about the same time but Big is moving a lot faster B. Big reaches the ground a lot sooner C. Little reaches the ground way before Big does D. Big and Little reach the ground at about the same time but Big is moving a lot slower E. Big and Little reach the ground at about the same time and they are moving at about the same speed

30. Solution 9... Apple tree Big apple is twice as big as Little apple. Both fall from the same height at the same time. Which statement is correct? A. Big and Little reach the ground at about the same time but Big is moving a lot faster B. Big reaches the ground a lot sooner C. Little reaches the ground way before Big does D. Big and Little reach the ground at about the same time but Big is moving a lot slower E. Big and Little reach the ground at about the same time and they are moving at about the same speed

31. Problem 10... Granny’s Orchard Big apple is twice as high as Little apple. They both fall at the same time. Let V B and V L denote their respective speeds just before hitting the ground. V B / V L is most nearly A. 1/2 B. 1 C. 1.5 D. 2 E. 4

32. Solution 10... Granny’s Orchard Big apple is twice as high as Little apple. They both fall at the same time. Let V B and V L denote their respective speeds just before hitting the ground. V B / V L is most nearly A. 1/2 B. 1 C. 1.5 D. 2 E. 4

33. Problem 11... Tippity-Top A stone is thrown straight up with a speed of 20 m/s. A. What is the speed at the tippity-top? B. What is the acceleration at the tippity-top? C. What is the time for the round trip? D. What is the total round trip distance?

34. Solution 11... Tippity-Top A stone is thrown straight up with a speed of 20 m/s. A. What is the speed at the tippity-top? 0 m/s B. What is the acceleration at the tippity-top? g=? C. What is the time for the round trip? 4 s D. What is the total round trip distance? 40 m

35. That’s all Folks!