Kinematics/Newton's Laws - The Burns Home Page

9/3/2009
Understanding
Kinematics/Newton’s Laws
Practice Questions
An object that’s moving with constant speed travels once
around a circular path. Which of the following is/are true
concerning this motion?
I The displacement is zero
II The average speed is zero
III The acceleration is zero
(a) I only
(b) I and II only
(c) I and III only
(d) III only
(e) II and III only
Understanding
Understanding
Which of the following is/are true?
I. If an object’s acceleration is constant, then it must
move in a straight line.
II. If an object’s acceleration is zero, then its speed must
remain constant.
III. If an object’s speed remains constant, then its
acceleration must be zero.
(a) I and II only
(b) I and III only
(c) II only
(d) III only
(e) II and III only
A baseball is thrown straight upward. What is the ball’s
acceleration at its highest point?
(a) 0
(b) ½ g [down]
(c) g [down]
(d) ½ g [up]
(e) g [up]
Gravity is always turned on.
1

9/3/2009
Understanding
Understanding
Hint:
How long would it take a car, starting from rest and
accelerating uniformly in a straight line at 5 m/s 2 , to cover
a distance of 200m?
1
s v0t at
2
(a) 9.0 s
(b) 10.5 s
(c) 12.0 s
(d) 15.5 s
(e) 20.0 s
2
m 1 m
200m 0 t 5
t
2
s 2 s
2 400m
t
m
5
2
s
t 8.9s
2
Hint:
A rock is dropped off a cliff and strikes the ground with an
impact of 30 m/s. How high was the cliff?
We need both the
initial and final velocity
in the equation
(a) 15.0 m
(b) 20 m
(c) 30 m
(d) 46 m
(e) 60 m
v v 2a s
2 2
f i
v v 2a s
2 2
f i
v v
s
2a
2 2
f i
2 2
m m
30 0
s s
m
29.8
2
s
45.9m
Understanding
Understanding
A stone is thrown horizontally with an initial speed of 10 m/s from a
bridge. If air resistance could be ignored, how long would it take the
stone to strike the water 80 m below the bridge?
Hint:
We need only think
about the vertical
components.
(a) 1 s
(b) 2 s
(c) 4 s
(d) 6 s
(e) 8 s
1
s v0t at
2
m 1 m
80m 0 t 9.8
t
2
s 2 s
2 160m
t
m
9.8
2
s
t 4.0s
2
2
A soccer ball, at rest on the ground, is kicked with an initial velocity of 10
m/s at a launch angle of 30 0 . Calculate its total flight time, assuming air
resistance is negligible?
Hint:
We need only think
about the vertical time
to travel up to its max
height, then double it.
(a) 0.5 s
(b) 1 s
(c) 1.7 s
(d) 2 s
(e) 4 s
v v at
f
i
vf
vi
t
a
m m
0 10 sin 30
s s
m
9.8
2
s
0.51s
2

9/3/2009
Understanding
A stone is thrown horizontally with an initial speed of 30 m/s from a
bridge. Find the stone’s total speed when it enters the water 4 seconds
later?
Hint:
We need only think
about the vertical time
to travel to find vertical
speed, then combine
with horizontal speed
(a) 30 m/ s
(b) 40 m/s
(c) 50 m/s
(d) 60 m/s
(e) 70 m/s
v v at
f
i
m m
vyf
0 9.8 2
4s
s s
m
39.2
s
v 2 2
f
vx vy
m
vxf
30
2 2
s
m m
39.2 30
2 2
s s
m
49.4
2
s
Understanding
Which of the following statements is true concerning the
motion of an ideal projectile launched at an angle of 45 0
to the horizontal?
(a) The acceleration vector points opposite to the
velocity vector on the way up and in the same
direction as the velocity vector on the way down.
(b) The speed at the top of the trajectory is zero.
(c) The object’s total speed remains constant during the
entire flight.
(d) The horizontal speed decreases on the way down.
(e) The vertical speed decreases on the way up and
increases on the way down.
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
20
velocity (m/s)
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
20
velocity (m/s)
10
10
time (s)
1 2 3 4 5 6 7
time (s)
1 2 3 4 5 6 7
−10
−10
−20
(a) Describe what happened to the car at time t=1 s
(b) How does the car’s average velocity between time t=0 sand t=1 s compare to its
average velocity between times t=1 s and t=5 s?
(c) What is the displacement of the car from time t=0 to time t=7s?
(d) Plot the car’s acceleration during this interval as a function of time.
(e) Plot the object’s position during this interval as a function of time. Assuming that
the car begins at s=0.
−20
(a) Describe what happened to the car at time t=1 s
The car’s velocity remains at 20 m/s, but the acceleration changes from
positive to negative at this time (the foot leaves the accelerator)
3

9/3/2009
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
20
velocity (m/s)
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
20
velocity (m/s)
10
10
time (s)
1 2 3 4 5 6 7
time (s)
1 2 3 4 5 6 7
−10
−10
−20
(b) How does the car’s average velocity between time t=0 sand t=1 s compare to its
average velocity between times t=1 s and t=5 s?
Between t=0 and t=1: the average velocity is ½(0 m/s + 20 m/s)=10 m/s
Between t=1 and t=5: the average velocity is ½(20m/s + 0m/s)=10 m/s
−20
(c) What is the displacement of the car from time t=0 to time t=7s?
Displacement is the net area between the graph as the time axis
Area=1/2(5*20) – ½(2*10) =40m
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
20
velocity 20 velocity (m/s) (m/s)
Understanding
This question concerns the motion of a car on a straight track; the car’s velocity
as a function of time is plotted below
50
velocity (m/s) 20 velocity (m/s)
10
10
40
10
time (s)
1 2 4 5 6 7
3 time (s)
1 2 3 4 5 6 7
30
time (s)
1 2 3 4 5 6 7
−10
20
−10
−10
−20
10
−20
−20
(d) Plot the car’s acceleration during this interval as a function of time.
time (s)
1 2 3 4 5 6 7
(e) Plot the object’s position during this interval as a function of time. Assuming that
the car begins at s=0.
4

9/3/2009
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
(a) Show that the cannonball will strike the wall.
(b) How long will it take for the cannonball to strike the wall?
(c) At what height above the base of the wall will the cannonball strike?
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
(a) Show that the cannonball will strike the wall.
1 2
x v0
xt
y v0
yt gt
2
x
2
t
x 1 x
v
v0
sin
2
0x
g
v0cos
2 v0cos
x
2
gx
v cos x tan
2 2
0
2v0
cos
m
2
9.8 2 220m
s
220m tan 40
2
m 2
250 cos 40
s
23m
v 2
sin 0 2
R
g
m
50 sin 240
s
R
m
9.8
2
s
251m
We need now only show that the
height of the ball is below 30 m
when the horizontal displacement
is 220m
This is less than 30 m, so contact
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
b) How long will it take for the cannonball to strike the wall?
x
t
v
0x
x
v cos 0
220m
m
50 cos40
s
5.7s
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
c) At what height above the base of the wall will the cannonball strike?
From (a) we have 23 m
5

9/3/2009
Understanding
A physics student is driving home after class. The car is travelling at 14.7 m/s
when it approaches an intersection. The student estimates that he is 20.0 m
from the entrance to the intersection (10.0 m wide) when the traffic light changes
from green to yellow. The light will change from yellow to red in 3.00 seconds.
The maximum safe deceleration of the car is 4.00 m/s 2 while the maximum
acceleration of the car is 2.00 m/s 2 . Should the physics student a) decelerate
and stop or b) accelerate and travel through the intersection? Note: there is a
police car directly behind the student.
Understanding
A physics student is driving home after class. The car is travelling at 14.7 m/s when it
approaches an intersection. The student estimates that he is 20.0 m from the entrance to
the intersection (10.0 m wide) when the traffic light changes from green to yellow. The light
will change from yellow to red in 3.00 seconds. The maximum safe deceleration of the car
is 4.00 m/s 2 while the maximum acceleration of the car is 2.00 m/s 2 . Should the physics
student a) decelerate and stop or b) accelerate and travel through the intersection? Note:
there is a police car directly behind the student.
Let’s try braking first and see how far the car travels before stopping.
Data Inventory
m
a 4.0
2
s
x 0m
i
m
vi
14.7
s
m
v
f
0
s
t 3.0 s
x ?
f
1 2
We shall use: x
f
xi vit at
2
m 1 m
x
f
0m 14.7 3.0s 4 3.0s
2
s 2 s
0m 44.1m 18.0m
26.1m
2
Therefore the student will travel 6.1 m into the intersection
(not good with police car behind him)
Understanding
A physics student is driving home after class. The car is travelling at 14.7 m/s when it
approaches an intersection. The student estimates that he is 20.0 m from the entrance to
the intersection (10.0 m wide) when the traffic light changes from green to yellow. The light
will change from yellow to red in 3.00 seconds. The maximum safe deceleration of the car
is 4.00 m/s 2 while the maximum acceleration of the car is 2.00 m/s 2 . Should the physics
student a) decelerate and stop or b) accelerate and travel through the intersection? Note:
there is a police car directly behind the student.
Now let’s try accelerating and see how far the car travels before the light turns red.
Data Inventory
m
a 2.0
2
s
x 0m
i
m
vi
14.7
s
v ?
f
t 3.0 s
x ?
f
1 2
We shall use: x
f
xi vit at
2
m 1 m
x
f
0m 14.7 3.0s
2.0 3.0s
2
s 2 s
0m 44.1m 9.0m
53.1m
2
Therefore the student will travel about 23 m past the
intersection before the light turns red.
Understanding
A car traveling at a constant speed of 30 m/s passes a highway patrol police car
which is at rest. The police officer accelerates at a constant rate of 3.0 m/s 2 and
maintains this rate of acceleration until he pulls next to the speeding car.
Assume that the police car starts to move at the moment the speeder passes
the car. Determine:
a) The time required for the police officer to catch the speeder?
b) The distance travelled during the chase?
6

9/3/2009
Understanding
A car traveling at a constant speed of 30 m/s passes a highway patrol police car which is
at rest. The police officer accelerates at a constant rate of 3.0 m/s 2 and maintains this rate
of acceleration until he pulls next to the speeding car. Assume that the police car starts to
move at the moment the speeder passes the car. Determine:
a) The time required for the police officer to catch the speeder?
Plan of attack: If we can find a position function for both the motorist and the
police car in terms of time, then we can set both functions equal to each other
(same position) and solve for time
Data Inventory motorist
m
a 0
2
s
x 0m
i
m
vi
30
s
m
v
f
30
s
t ?
x ?
f
x x vt
f
i
m
x
f
0m 30 t
s
m
xf
30 t
s
Data Inventory Police
m
a 3.0
2
s
x 0m
i
m
vi
0
s
v ?
f
t ?
x ?
f
1
x
f
xi vit at
2
m 1 m
x
f
0m 0 t 3.0
t
2
s 2 s
m 2
xf
1.5 t
2
s
2
2
Let’s set then equal and solve
m m
2
30 t
1.5
t
2
s s
m m
0 30 t
1.5 t
s s
2
2
m m
0 t
30 1.5 t
2
s s
Understanding
Therefore the police car catches up with
the speeder at 20s (the 0s is when the
car initially passes the police car)
Therefore
t 0
or
m m
30 1.5 0
2 t
s s
m m
1.5 t 30
2
s s
m
30
t s
m
1.5
2
s
20s
Understanding
Understanding
A car traveling at a constant speed of 30 m/s passes a highway patrol police car which is
at rest. The police officer accelerates at a constant rate of 3.0 m/s 2 and maintains this rate
of acceleration until he pulls next to the speeding car. Assume that the police car starts to
move at the moment the speeder passes the car. Determine:
b) The distance travelled during the chase?
A stone is thrown vertically upward from the edge of a building 19.6 m high with
an initial velocity of 14.7 m/s. The stone just misses the building on the way
down and strikes the street below. Determine:
a) The time of flight?
b) The velocity of the stone just before it strikes the ground ?
Since we know the time (20s) from part a), we need only plug it into the
distance formula from either car. [let’s use the speeder ]
x
f
vt
m
30 20s
s
600m
7

9/3/2009
Understanding
Understanding
A stone is thrown vertically upward from the edge of a building 19.6 m high with
an initial velocity of 14.7 m/s. The stone just misses the building on the way
down and strikes the street below. Determine:
a) The time of flight?
Given:
Required:
m
vi
14.7
s
m
a 9.80
2
s
x 19.6m
i
x 0m
f
t
Relationship:
Work:
1
x
f
xi vit at
2
2
1 2
x
f
xi vit at
2
1
0
2
2
at vit xi x
f
2 1
vi vi 4
a 2
xi x
f
t
1
2
a
2
2
v vi 2a xi x
f
a
2
m m m
14.7 14.7 2 9.8 2 19.6m
0m
s s s
m
9.8
2
s
Therefore
t 1s
t 4s
Flight time is 4 s
A stone is thrown vertically upward from the edge of a building 19.6 m high with
an initial velocity of 14.7 m/s. The stone just misses the building on the way
down and strikes the street below. Determine:
b) The velocity of the stone just before it strikes the ground ?
m
v 14.7
Given: i
s
Work:
m
a 9.80
2
s
v vi
at
f
xi
19.6m
m m
14.7 9.
80 2 4.
0s
xf
0m
s s
t 4s
Required: v
f
Relationship:
m
245
.
s
The negative value in the velocity indicates that
the stone is travelling downward.
v
f
vi
at
`
8