# = 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

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1 Secton 1.3: Acceleraton Tutoral 1 Practce, page Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement: The rock s average acceleraton s 1.20 m/s 2 [S]. 2. Gven: 17 m/s [N]; 25 m/s [N]; t 12 s Requred: Analyss: v t v t 25 m/s [N] 17 m/s [N] 12 s 8 m/s [N] 12 s 0.67 m/s 2 [N] Statement: The car s average acceleraton s 0.67 m/s 2 [N]. 3. Gven: 25 m/s [W]; 29 m/s [E]; t 0.25 s Requred: Analyss: v t v t 29 m/s [E] 25 m/s [W] 0.25 s 29 m/s [E] + 25 m/s [E] 0.25 s 54 m/s [E] 0.25 s 220 m/s 2 [E] Statement: The squash ball s average acceleraton s 220 m/s 2 [E] or m/s 2 [E]. Tutoral 2 Practce, page Gven: 3.2 m/s [W]; 5.8 m/s [W]; 1.23 m/s 2 [W] Requred: t Analyss: a av t v t f v t v 5.8 m/s [W] 3.2 m/s [W] 1.23 m/s 2 [W] 2.6 m [W] s 1.23 m s [W] 2 t 2.1 s Statement: The rado-controlled car s acceleraton wll take 2.1 s. 2. Gven: 17 m/s [W]; 2.4 m/s 2 [W]; t 6.2 s Requred: Analyss: t t t v f v v f a av t 17 m/s [W] 2.4 m s [W] 2 ' 6.2 s ( ) 17 m/s [W] m/s [W] (two extra dgts carred) 2.1 m/s [W] Statement: The ntal velocty of the speedboat was 2.1 m/s [W]. Tutoral 3 Practce, page (a) Gven: b 4.0 s; h 8.0 m/s [S] Requred: d Analyss: d A trangle Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-1

2 d A trangle B. Postve velocty value: 1 2 bh ( ) 8.0 m s [S] s d 16 m [S] Statement: The object has travelled 16 m [S] after 4.0 s. (b) Gven: b 5.0 s; h 10.0 m/s [S]; l 2.5 s; w 10.0 m/s [S] Requred: d Analyss: d A trangle d A trangle 1 bh + lw 2 ( ) 10.0 m s [S] s 25.0 m [S] m [S] s ( ) 10.0 m s [S] d 50 m [S] Statement: The object has travelled 50 m [S] after 7.5 s. Negatve velocty value: Mn Investgaton: Moton Smulatons, page 27 A. Postve velocty value: The poston tme graph wll be a straght lne startng at the orgn wth a postve slope. The velocty tme graph wll be a horzontal lne wth postve value. Negatve velocty value: The poston tme graph wll be a straght lne startng at the orgn wth a negatve slope. The velocty tme graph wll be a horzontal lne wth negatve value. Negatve ntal poston, postve velocty value: The poston tme graph wll be a straght lne startng below the x-axs wth a postve slope. The velocty tme graph wll be a horzontal lne wth postve value. Negatve ntal poston, negatve velocty value: The poston tme graph wll be a straght lne startng below the x-axs wth a negatve slope. The velocty tme graph wll be a horzontal lne wth negatve value. Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-2

3 Negatve ntal poston, postve velocty value: Negatve ntal poston, negatve velocty value: C. Dfferences are due to the dffculty n usng the mouse to mmc constant velocty. Tutoral 4 Practce, page (a) Gven: t 1.0 s; poston tme graph Requred: nst Analyss: nst tangent to the curve at t 1.0 s, so m d t. By placng a ruler along the curve n Fgure 6 at t 1.0 s, I can pcture the tangent. The tangent has a rse of 4.0 m [E] over a run of 2.0 s. m d t 4.0 m [E] m 2.0 s nst 2.0 m/s [E] object at 1.0 s s 2.0 m/s [E]. (b) Gven: t 3.0 s; poston tme graph Requred: nst Analyss: nst tangent to the curve at t 3.0 s, so m d t. By placng a ruler along the curve n Fgure 6 at t 3.0 s, I can pcture the tangent. The tangent has a rse of 12.0 m [E] over a run of 2.0 s. m d t 12.0 m [E] m 2.0 s nst 6.0 m/s [E] object at 3.0 s s 6.0 m/s [E]. (c) At t 1.0 s, nst s 2.0 m/s [E], at t 2.0 s, nst s 4.0 m/s [E], and at t 3.0 s, nst s 6.0 m/s [E]. Snce the ncrease n the nstantaneous velocty s constant (2.0 m/s [E] every second), t s possble that the object s movng wth constant acceleraton. 2. (a) Gven: t 5.0 s; poston tme graph Requred: nst Analyss: nst tangent to the curve at t 5.0 s, so m d t. By placng a ruler along the curve n Fgure 7 at t 5.0 s, I can pcture the tangent. The tangent has a rse of 150 m [E] over a run of 5.0 s. m d t 150 m [E] 5.0 s nst 30 m/s [E] object at 5.0 s s 30 m/s [E]. Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-3

4 (b) Gven: d m [E]; m [E]; t s; 10.0 s Requred: Analyss: v av d t d 1 t 1 d 1 v av t m [E] 0.0 m [E] 10.0 s 0.0 s 30 m/s [E] Statement: The average velocty of the object over the tme nterval from 0.0 s to 10.0 s s 30 m/s [E]. (c) When an object s acceleratng unformly (constant acceleraton), the average velocty over an nterval of tme equals the nstantaneous velocty of the mdpont n that nterval of tme. Secton 1.3 Questons, page Answers may vary. Sample answer: An acceleratng object may exhbt ncreasng velocty, such as a horse acceleratng from a slow trot to a gallop. An acceleratng object may exhbt decreasng velocty, such as a cyclst who slows down whle rdng up a steep road. An acceleratng object may come to a complete stop, such as a car travellng east that accelerates west untl t stops. 2. Answers may vary. Sample answer: To determne the acceleraton of an object from a velocty-tme graph, dvde the velocty by the tme at a gven pont. 3. Answers may vary. Sample answer: To determne the dsplacement of an object from a velocty tme graph, calculate the area under the graph from the ntal tme to the fnal tme. The area s equal to the dsplacement between those two tmes. 4. (a) Gven: v 28 m/s [E]; t 7.0 s Requred: Analyss: a av v t a av v t 28 m/s [E] 7.0 s 4.0 m/s 2 [E] Statement: The average acceleraton descrbed by the graph s 4.0 m/s 2 [E]. (b) Gven: v 24.5 m/s [E]; t 7.0 s Requred: Analyss: a av v t a av v t 24.5 m/s [E] 7.0 s 3.5 m/s 2 [E] Statement: The average acceleraton descrbed by the graph s 3.5 m/s 2 [E]. (c) Gven: v 2.1 m/s [E]; t 7.0 s Requred: Analyss: a av v t a av v t 2.1 m/s [E] 7.0 s 0.30 m/s 2 [E] Statement: The average acceleraton descrbed by the graph s 0.30 m/s 2 [E]. 5. Answers may vary. Sample answer: What you sad about the constant speed of the object sn t rght. Even though the speed s stll the same, the drecton has changed from north to south. That means that the velocty has changed, so there must have been an acceleraton n the drecton of south. 6. (a) In the frst segment, the object accelerates from 0.0 m/s to 6.0 m/s [W] n the frst 4.0 s. In the second segment, the object contnues at a constant velocty of 6.0 m/s [W] for 3.0 s. In the thrd segment, the object accelerates east so the velocty changes from 60.0 m/s [W] to 0.0 m/s n the fnal 3.0 s. Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-4

5 (b) For the frst segment: Gven: v 6.0 m/s [W]; t 4.0 s Requred: Analyss: a av v t a av v t 6.0 m/s [W] 4.0 s 1.5 m/s 2 [W] Statement: The average acceleraton n the frst segment of the graph s 1.5 m/s 2 [W]. For the second segment: Gven: v 0.0 m/s; t 3.0 s Requred: Analyss: a av v t a av v t 0.0 m/s 4.0 s 0.0 m/s 2 Statement: The average acceleraton n the second segment of the graph s 0.0 m/s 2. For the thrd segment: Gven: v 6.0 m/s [W]; t 3.0 s Requred: Analyss: a av v t a av v t 6.0 m/s [W] 3.0 s 6.0 m/s [E] 3.0 s 2.0 m/s 2 [E] Statement: The average acceleraton n the thrd segment of the graph s 2.0 m/s 2 [E]. (c) Gven: b s; b s; h 6.0 m/s [W]; l 3.0 s Requred: d Analyss: d A trangle 1 + A trangle 2 d A trangle 1 + A trangle b 1 h + lh b 2 h ( ) 6.0 m s [W] s s s ( ) 6.0 m s [W] ( ) 6.0 m s [W] 12 m [W] + 18 m [W] + 9 m [W] d 39 m [W] Statement: The object has travelled 39 m [W] after 10.0 s. 7. Gven: 2.0 m/s [W]; 4.5 m/s [W]; t 1.9 s Requred: Analyss: v t v t 4.5 m/s [W] 2.0 m/s [W] 1.9 s 2.5 m/s [W] 1.9 s 1.3 m/s 2 [W] Statement: The average acceleraton of the car s 1.3 m/s 2 [W]. 8. Gven: 0.68 m/s [N]; 0.89 m/s [N]; 0.53 m/s 2 [N] Requred: t Analyss: a av t v t f v t v 0.89 m/s [N] 0.68 m/s [N] 0.21 m [N] s 0.53 m s [N] m/s 2 [N] t 0.40 s Statement: It wll take 0.40 s to ncrease the bcycle s velocty. Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-5

6 9. (a) Gven: 0.0 m/s; 2.90 m/s 2 [S]; t 5.72 s Requred: Analyss: t t v f v v f a av t t 0.0 m/s 2.90 m s [S] 2 ' 5.72 s 0.0 m/s 16.6 m/s [S] 16.6 m/s [N] ( ) Statement: The ntal velocty of the car was 16.6 m/s [N]. (b) To decrease the velocty, the drver must accelerate n the opposte drecton. In ths example, to stop gong north, the drver accelerated south. 10. Gven: 6.0 m/s [E]; 7.3 m/s [W]; t s Requred: Analyss: v t v t 7.3 m/s [W] 6.0 m/s [E] s 7.3 m/s [W] m/s [W] s 13.3 m/s [W] s 140 m/s 2 [W] Statement: The average acceleraton of the tenns ball s 140 m/s 2 [W] or m/s 2 [W]. 11. (a) Gven: t 6.0 s; poston tme graph Requred: nst Analyss: nst tangent to the curve at t 6.0 s, so m d t. By placng a ruler along the curve n Fgure 9 at t 6.0 s, I can pcture the tangent. The tangent has a rse of 120 m [E] over a run of 5.0 s. m d t 120 m [E] m 5.0 s nst 24 m/s [E] object at 6.0 s s 24 m/s [E]. (b) Gven: d m; 200 m; t s; 10.0 s Requred: Analyss: v av d t d 1 t 1 d 1 v av t m [W] 0.0 m [W] 10.0 s 0.0 s 20 m/s [W] Statement: The average velocty of the object over the tme nterval from 0.0 s to 10.0 s s 20 m/s [W]. Copyrght 2011 Nelson Educaton Ltd. Chapter 1: Moton n a Straght Lne 1.3-6

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