Physics 221 Chapter 2 Speed Speed Distance Time

Physics 221 Chapter 2

Speed • Speed = Distance / Time • v = d/t

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. B. C. D. 50 m. p. h. 63. 3 m. p. h. 70 m. p. h

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. B. C. D. 50 m. p. h. 63. 3 m. p. h. 70 m. p. h

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!

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

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

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.

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!

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? A C B

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? ) C A B

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

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?

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=5 s is 30 m/s

Acceleration • Acceleration is the rate of change of velocity • a = ( vf - v i ) / t

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

Solution 4. . . Translational Motion ©Q. Is the speed constant at t=10 s? N 0! ©Q. When is the acceleration zero? 15 s, 20 s, etc. ©Q. When is it slowing down (decelerating)? 45 s, 50 s etc. ©Q. What is the acceleration at t=7 s? 1 m/s 2

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

Solution 5 a • • • 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 (Vf - Vi) x t d = 54 m

Solution 5 b • a = (Vf - Vi ) / t • a = 3 m/s 2 • Vf = V i + a t • Vf = 0 + 3 x 4 • Vf at 4 s = 12 m/s

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

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

Equation Summary for uniform acceleration (No Jerks Pleeeease!) • Vf = V i + a t • d = Vi t + 1/2 a t 2 • Vf 2 = Vi 2 + 2 ad • Vave = (Vf + Vi) / 2

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?

Solution 7 • The equation that comes to our rescue is: • Vf 2 = Vi 2 + 2 ad • (24 )2= (0)2 + 2 a(72) • a = 4 m/s 2

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?

Solution 8. . . Free fall • Vf = V i + a t • (a) Vf = 0 + (9. 8)(3) • Vf = 29. 4 m/s • (b) d = Vi t + 1/2 a t 2 • d = 0 + (1/2)(9. 8)(9) • d = 44. 1 m

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

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

Problem 10. . . Granny’s Orchard • Big apple is twice as high as Little apple. They both fall at the same time. Let VB and VL denote their respective speeds just before hitting the ground. VB / VL is most nearly • • • A. 1/2 B. 1 C. 1. 5 D. 2 E. 4

Solution 10. . . Granny’s Orchard • Big apple is twice as high as Little apple. They both fall at the same time. Let VB and VL denote their respective speeds just before hitting the ground. VB / VL is most nearly • • • A. 1/2 B. 1 C. 1. 5 D. 2 E. 4

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?

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

That’s all Folks!