Section 1.1: Motion and Motion Graphs
Tutorial 1 Practice, page 10
1. (a) Given: !d1 = 1.2 !t1 = i !d2 = 1.2 !t2 = in
Required: va)
Analysis: Calculate the total distance tra)elled, !d = !d1 + !d2 , and the total time
!d
taken, !t = !t1 + !t2 . Then, use the equation va) = to calculate the a)erage speed.
!t
1h
!t1 = min "
/0 min
!t1 = h
!t2 = h
Solution: !d = !d1 + !d2
= 1.2 km + 1.2 km
!d = km
!t = !t1 + !t2
= h+ h
!t = h
!d
va) =
!t
km
=
h
va) = km h
Statement: The r a)erage speed
(b) Given: !d = 1.2 km E !t = min
!
Required: va)
!
! !d
Analysis: The a)erage )elocity is the ratio of the displacement and the time taken, va) = .
!t
1h
!t = min "
/0 min
!t = h
!
! !d
Solution: va) =
!t
1.2 km E
=
h
!
va) = 3.0 km E
Statement: The a)erage )elocity from the house to the farthest position from the house is
3.0
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-1
, r r
(c) Given: !d1 = 1.2 km E !t1 = !d2 = 1.2 km !t2 = h
!
Required: va)
Analysis: Since the two displacements are equal in magnitude and opposite in direction, the total
Statement:
(d)
A)erage )elocity depends on displacement, which is a )ector quantity. Since the displacements
are not the same, the a)erage )elocities are not the same.
!
2. Given: v = m s forwar !t = 0.32 s
!
Required: !d
!
! !d r r r
Analysis: Rearrange va) = to sol)e for !d: !d = va) !t.
r r !t
Solution: !d = va) !t
= ( m s 4forward5(0.32 s
r
!d = m 4forward5
Statement: The bus mo)es 8./ m 4forward5 before the dri)er reacts.
3. Given: !d = 200 laps, at la !t = h
Required: va) in
!d
Analysis: va) = .
!t
km !d
Solution: !d = 200 laps " va) =
1 lap !t
km
!d = km =
h
va) = 1.20 " 102 km h
Statement: The a)erage speed of a dri)er who completes 200 laps in /./9 h is 1.20 ! 102 km h .
4. (a) Given: !d1 = m !t1 = s !d2 = m !t2 = 21 s
r
Required: va)
Analysis: Calculate the total distance walked, !d = !d1 + !d2 , and the time
!d
taken, !t = !t1 + !t2 . Then, calculate the a)erage speed using va) = .
!t
!d
Solution: !d = !d1 + !d2 !t = !t1 + !t2 va) =
!t
= m+ m = s + 21 s m
!d = m !t = 8/ s =
s
va) = ms
Statement:
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-2
, ! !
(b) Given: !d1 = m 4E5 !t1 = s !d2 = m 4 5 !t2 = 21 s
r
Required: va)
! ! !
Analysis: Calculate the total displacement, !d = !d1 + !d2 . Then, calculate the a)erage )elocity
!
! !d
using va) = . Use east as positi)e.
!t
!
! ! ! ! !d
Solution: !d = !d1 + !d2 va) =
!t
= m + (" m m 4E5
=+ m =
! s
!d = m 4E5 !
va) = 1.2 m s 4E5
Statement: The stud
! !
5. (a) Given: !d1 = /2 km 4S5 !d2 = m 4N5 va) = km h
!
Required: va)
!d
Analysis: Use the total distance, !d = !d1 + !d2 , and a)erage speed, va) = , to determine the
!t
! ! !
time taken for the trip, !t . Then, determine the total displacement, !d = !d1 + !d2 . Then
!
! !d
calculate the a)erage )elocity using va) = . Use north as positi)e.
!t
!d
Solution: !d = !d1 + !d2 va) =
!t
= /2 km + km !d
= km !t =
va)
!d = km
km
=
km h
!t = h (two eGtra digits carrie
!
! ! ! ! !d
!d = !d1 + !d2 vav =
!t
= ("62 km) + (+78 km) 16 km [N]
= +16 km =
! 2.545 h
!d = 16 m [N] !
vav = 6.3 km/h [N]
Statement:
(b) Answers may )ary. Sample answer: The truck turned around at one point during its trip. At
the end, it was only 1/ km away from where it started. As a result, the magnitude of the a)erage
)elocity is quite low compared to the a)erage speed.
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-3
, Tutorial 2 Practice, page 13
1. (a) Velocity is slope on a position–
the )elocity is increasing.
(b)
2. Answers may )ary. Sample answers:
(a) Initially, the )elocity is large and constant in the east direction. Then, it is lower and constant
in the east direction. Calculate the slope of each section of the position–time graph using data
from the graph.
t (s) 0.0 0.2 0.8
!
d (m [E]) 0.0 20 30
! !
r ___ !d 20 " 0.0 !d " 20
v (m/h [E]) = = 100 = =
!t 0.2 " 0.0 !t " 0.2
Use these )elocity data to draw a )elocity–time graph.
(b) Initially the )elocity is large and constant in a west direction, then it is zero and finally it i s
low and constant in an east direction. Calculate the slope of each section of the position–time
graph using data from the graph.
t (h) 0.0 1.0 2.0
!
d ( [ ) 0.0 0.0
! ! !
! ___ !d " 0.0 !d " !d 0.0 "
v (m/h [W]) = = = =0 = ="
!t " 0.0 !t 1.0 " !t 2.0 " 1.0
Use these )elocity data to draw a )elocity–time graph.
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-
Tutorial 1 Practice, page 10
1. (a) Given: !d1 = 1.2 !t1 = i !d2 = 1.2 !t2 = in
Required: va)
Analysis: Calculate the total distance tra)elled, !d = !d1 + !d2 , and the total time
!d
taken, !t = !t1 + !t2 . Then, use the equation va) = to calculate the a)erage speed.
!t
1h
!t1 = min "
/0 min
!t1 = h
!t2 = h
Solution: !d = !d1 + !d2
= 1.2 km + 1.2 km
!d = km
!t = !t1 + !t2
= h+ h
!t = h
!d
va) =
!t
km
=
h
va) = km h
Statement: The r a)erage speed
(b) Given: !d = 1.2 km E !t = min
!
Required: va)
!
! !d
Analysis: The a)erage )elocity is the ratio of the displacement and the time taken, va) = .
!t
1h
!t = min "
/0 min
!t = h
!
! !d
Solution: va) =
!t
1.2 km E
=
h
!
va) = 3.0 km E
Statement: The a)erage )elocity from the house to the farthest position from the house is
3.0
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-1
, r r
(c) Given: !d1 = 1.2 km E !t1 = !d2 = 1.2 km !t2 = h
!
Required: va)
Analysis: Since the two displacements are equal in magnitude and opposite in direction, the total
Statement:
(d)
A)erage )elocity depends on displacement, which is a )ector quantity. Since the displacements
are not the same, the a)erage )elocities are not the same.
!
2. Given: v = m s forwar !t = 0.32 s
!
Required: !d
!
! !d r r r
Analysis: Rearrange va) = to sol)e for !d: !d = va) !t.
r r !t
Solution: !d = va) !t
= ( m s 4forward5(0.32 s
r
!d = m 4forward5
Statement: The bus mo)es 8./ m 4forward5 before the dri)er reacts.
3. Given: !d = 200 laps, at la !t = h
Required: va) in
!d
Analysis: va) = .
!t
km !d
Solution: !d = 200 laps " va) =
1 lap !t
km
!d = km =
h
va) = 1.20 " 102 km h
Statement: The a)erage speed of a dri)er who completes 200 laps in /./9 h is 1.20 ! 102 km h .
4. (a) Given: !d1 = m !t1 = s !d2 = m !t2 = 21 s
r
Required: va)
Analysis: Calculate the total distance walked, !d = !d1 + !d2 , and the time
!d
taken, !t = !t1 + !t2 . Then, calculate the a)erage speed using va) = .
!t
!d
Solution: !d = !d1 + !d2 !t = !t1 + !t2 va) =
!t
= m+ m = s + 21 s m
!d = m !t = 8/ s =
s
va) = ms
Statement:
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-2
, ! !
(b) Given: !d1 = m 4E5 !t1 = s !d2 = m 4 5 !t2 = 21 s
r
Required: va)
! ! !
Analysis: Calculate the total displacement, !d = !d1 + !d2 . Then, calculate the a)erage )elocity
!
! !d
using va) = . Use east as positi)e.
!t
!
! ! ! ! !d
Solution: !d = !d1 + !d2 va) =
!t
= m + (" m m 4E5
=+ m =
! s
!d = m 4E5 !
va) = 1.2 m s 4E5
Statement: The stud
! !
5. (a) Given: !d1 = /2 km 4S5 !d2 = m 4N5 va) = km h
!
Required: va)
!d
Analysis: Use the total distance, !d = !d1 + !d2 , and a)erage speed, va) = , to determine the
!t
! ! !
time taken for the trip, !t . Then, determine the total displacement, !d = !d1 + !d2 . Then
!
! !d
calculate the a)erage )elocity using va) = . Use north as positi)e.
!t
!d
Solution: !d = !d1 + !d2 va) =
!t
= /2 km + km !d
= km !t =
va)
!d = km
km
=
km h
!t = h (two eGtra digits carrie
!
! ! ! ! !d
!d = !d1 + !d2 vav =
!t
= ("62 km) + (+78 km) 16 km [N]
= +16 km =
! 2.545 h
!d = 16 m [N] !
vav = 6.3 km/h [N]
Statement:
(b) Answers may )ary. Sample answer: The truck turned around at one point during its trip. At
the end, it was only 1/ km away from where it started. As a result, the magnitude of the a)erage
)elocity is quite low compared to the a)erage speed.
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-3
, Tutorial 2 Practice, page 13
1. (a) Velocity is slope on a position–
the )elocity is increasing.
(b)
2. Answers may )ary. Sample answers:
(a) Initially, the )elocity is large and constant in the east direction. Then, it is lower and constant
in the east direction. Calculate the slope of each section of the position–time graph using data
from the graph.
t (s) 0.0 0.2 0.8
!
d (m [E]) 0.0 20 30
! !
r ___ !d 20 " 0.0 !d " 20
v (m/h [E]) = = 100 = =
!t 0.2 " 0.0 !t " 0.2
Use these )elocity data to draw a )elocity–time graph.
(b) Initially the )elocity is large and constant in a west direction, then it is zero and finally it i s
low and constant in an east direction. Calculate the slope of each section of the position–time
graph using data from the graph.
t (h) 0.0 1.0 2.0
!
d ( [ ) 0.0 0.0
! ! !
! ___ !d " 0.0 !d " !d 0.0 "
v (m/h [W]) = = = =0 = ="
!t " 0.0 !t 1.0 " !t 2.0 " 1.0
Use these )elocity data to draw a )elocity–time graph.
Copyright © 2012 Nelson Education Ltd. Chapter 1: Kinematics 1.1-
