Kinematics Review

35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 What time interval (if any) has negative velocities in positive positions? What time interval(s) if any has a positive acceleration? Does the object ever change directions? What is the total distance for the 40 seconds? Construct a VT graph that shows the same motion as this DT graph.

35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 What time interval (if any) has negative velocities in positive positions? What time interval(s) if any has a positive acceleration? Does the object ever change directions? What is the total distance for the 40 seconds? Construct a VT graph that shows the same motion as this DT graph.

2 If an object travels 78.4 km/hr for 45 min, and then 50.0 km/hr for 20.0 km, what was the average velocity for the whole trip?

An object is tossed 24.0 m/s upward. How high does it go? 3 An object is tossed 24.0 m/s upward. How high does it go?

4 Sketch a VT graph for each DT graph: A. B. C.

5 What is the total distance for the 20 s? 35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 VELOCITY (m/s) TIME (s) What is the total distance for the 20 s? What is the displacement for the 20 s?

6 Two objects start at the same place and travel 300 m. Both start from rest at the same time and reach 300m at the same time. One object travels at constant speed, and the other accelerates. If the first object has an acceleration of 4 m/s2, what must the constant speed of the other object be?

7 What was the initial velocity of a ball thrown from a 80.0 m tall cliff, if it strikes the base of the cliff with a velocity of 62.0 m/s?

THINKER QUESTION: 8 A brick is dropped from rest from the top of a 40 m tall building. On the way down it is observed passing a 1.2 m tall window in .10 s. What is the height of the bottom of the window? 40 m ?

Now you will check and correct your answers Take the time to really understand each problem

1 ANSWER : 32-40 s DISTANCE ( m ) TIME (s) 35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 What time interval (if any) has negative velocities in positive positions? ANSWER : 32-40 s

1 ANSWER: 4 – 12 s DISTANCE ( m ) TIME (s) 35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 + direction + faster & faster + a B. What time interval(s) if any has a positive acceleration? ANSWER: 4 – 12 s

1 ANSWER: Yes , at t = 32s it starts going in the negative direction 35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 C. Does the object ever change directions? ANSWER: Yes , at t = 32s it starts going in the negative direction

1 10 m 30 m 35 m ANSWER: 75 m DISTANCE ( m ) TIME (s) 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 30 m TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 35 m D. What is the total distance for the 40 seconds? ANSWER: 75 m

35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 (28,30) 1 (38, 25) (40, 20) TIME (s) DISTANCE ( m ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 (22,-15) (12,-30) E. Construct a VT graph that shows the same motion as this DT graph. Find velocity (slope): Find velocity (slope): Find velocity (slope): -15 – (-30) 15 22 – 12 10 V = ________ = _____ = 1.5 m/s 30 - (-15) 45 28 - 22 6 V = ________ = _____ = 7.5 m/s 25 - 20 5 38 - 40 -2 V = ________ = _____ = - 2.5 m/s

1 VELOCITY( m/s ) TIME (s) 8 7 6 5 4 3 2 1 -1 -2 -3 1 TIME (s) VELOCITY( m/s ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 E. Construct a VT graph that shows the same motion as this DT graph. Find velocity (slope): Find velocity (slope): Find velocity (slope): -15 – (-30) 15 22 – 12 10 V = ________ = _____ = 1.5 m/s 30 - (-15) 45 28 - 22 6 V = ________ = _____ = 7.5 m/s 25 - 20 5 38 - 40 -2 V = ________ = _____ = - 2.5 m/s

If an object travels 78. 4 km/hr for 45 min, and then 50 If an object travels 78.4 km/hr for 45 min, and then 50.0 km/hr for 20.0 km, what was the average velocity for the whole trip? 2 First Part The Rest Whole Trip d d d t t t v = v = v = d 20 .75 t 78.8 78.4 = 50.0 = v = In hr 1.15 Solve: d = 58.8 km Solve: t = .4 hr Solve: V = 68.5 km/hr

An object is tossed 24.0 m/s upward. How high does it go? 3 So right here I set my frame of reference…UP is positive vi = 24 vf2 = vi2 + 2ad 0 = 242 + 2(-9.8)d 0 = 576 - 19.6d 19.6d = 576 d = 29.4 m + Pos direction - Getting slower a = -9.8 Goes UP until it stops! vf = 0 d = ?

4 Sketch a VT graph for each DT graph: A. B. C.

5 What is the total distance for the 20 s? You do NOT have to split them The way that I did – as long As you have all rectangles And triangles We should get the same answers 5 35 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 -35 -40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 225 62.5 10 90 VELOCITY (m/s) TIME (s) What is the total distance for the 20 s? What is the displacement for the 20 s? 30 + 225 + 62.5 + 10 + 10 + 90 = 427.5 m 10 + 10 + 90 – 30 – 225 – 62.5 = - 207.5 m

6 Constant Speed Object d t v = Accelerating Object vi = 0 d = 300 Two objects start at the same place and travel 300 m. Both start from rest at the same time and reach 300 m at the same time. One object travels at constant speed, and the other accelerates. If the first object has an acceleration of 4 m/s2, what must the constant speed of the other object be? 6 Constant Speed Object d t v = Accelerating Object vi = 0 d = 300 a = 4 t = ? d = vit + ½ at2 300 = ½ (4)t2 t = 12.2 s 300 12.2 v = v = 24.6 m/s

7 vf2 = vi2 + 2ad 622 = vi2 + 2(9.8)(80) vi = +- 47.7 m/s What was the initial velocity of a ball thrown from a 80.0 m tall cliff, if it strikes the base of the cliff with a velocity of 62.0 m/s? vi = ? d = 80 so down is POS a = 9.8 vf = 62 vf2 = vi2 + 2ad 622 = vi2 + 2(9.8)(80) vi = +- 47.7 m/s

8 32.0m THINKER QUESTION: Passing window: From top of building: d = ? A brick is dropped from rest from the top of a 40 m tall building. On the way down it is observed passing a 1.2 m tall window in .10 s. What is the height of the bottom of the window? Passing window: From top of building: d = ? a = 9.8 vf = 11.5 vi = 0 d = 1.2 a = 9.8 t = .10 vi = ? 32.0m d = vit + ½ at2 vf2 = vi2 + 2ad 40 m 1.2 = vi(.10) + ½ (9.8)(.10)2 11.52 = 2(9.8)d ? vi = 11.5 m/s d = 6.76 m