•
•
•
What part has zero acceleration?
Where is the object stationary?
Is there a region of constant acceleration?
•
•
•
What part has zero acceleration? Only if not turning
Where is the object stationary? Only at t = 0
Is there a region of constant acceleration?
If not turning, a = 0 in circled region, however
there is no nonzero constant-a region (1D case)
•
•
What is the acceleration in this situation?
The skydiver then pulls his parachute at an
altitude of 860 m and drops to the ground
according to:
y=860 m – (50 m/s×t) + (0.025 m/s3×t3)
a.
Find velocity and acceleration 20 seconds
later.
b. Draw vectors for these quantities at this time.
•
•
What is the acceleration in this situation? Zero.
The skydiver then pulls his parachute at an
altitude of 860 m and drops to the ground
according to:
y=860 m – (50 m/s×t) + (0.025 m/s3×t3)
a.
Find velocity and acceleration 20 seconds
later. vy = -20 m/s; ay = +3 m/s2
b. Draw vectors for these quantities at this time.
A bullet is fired horizontally with an initial velocity of vx from
a tower height D. If air resistance is neglected, find the
horizontal distance the bullet will travel before hitting the
ground.
A bullet is fired horizontally with an initial velocity of vx from
a tower height D. If air resistance is neglected, find the
horizontal distance the bullet will travel before hitting the
ground.
2D
2D
t=
; x = vx
g
g
Consider the following vectors in the x-y plane: A = 5.0 m/s
at 45 degrees and B = 2.5 m/s at 135 degrees.
a) Add the two vectors and determine the resultant.
b) Find the cross product.
Consider the following vectors in the x-y plane: A = 5.0 m/s
at 45 degrees and B = 2.5 m/s at 135 degrees.
a) Add the two vectors and determine the resultant.
b) Find the cross product.
A + B = (1.8 ms ,5.3 ms )
m2 ˆ
A × B = (12.5 2 )k
s
v avg = distance
time
=0.2 mile/minute
zero!
Not like acceleration vector.
•
Find final v if starting from rest?
•
Find final v if starting from rest?
–
Integration needed:
9s
vx = vo + ∫ ax dt = 50m/s
0
–
(Also note that the integral is the area under the curve)
A golf ball is hit from the ground with speed v. In order that
it will travel a distance d (in absence of air friction), find the
launch angle θ.
From the top of a building of height h, Zelda drops a
projectile at time t = 0. 1.0 s later her friend Zeke drops a
similar projectile from a window at a height of exactly h/2.
The projectiles hit each other at the instant they reach the
bottom of the building. Find the time for Zelda’s projectile to
fall, and the height of the building.
A golf ball is hit from the ground with speed v. In order that
it will travel a distance d (in absence of air friction), find the
launch angle θ.
2v 2
v2
d=
cos θ sin θ = sin 2θ
g
g
 gd 
solve ⇒ θ = sin  2 
v 
1
2
−1
From the top of a building of height h, Zelda drops a
projectile at time t = 0. 1.0 s later her friend Zeke drops a
similar projectile from a window at a height of exactly h/2.
The projectiles hit each other at the instant they reach the
bottom of the building. Find the time for Zelda’s projectile to
fall, and the height of the building.
t = 3.4s, h = 57m
Formula sheet (exam 1):
d 2x d 2
ax = 2 = 2 3.00t 2 = 6.00
dt
dt
d2y
d2
a y = 2 = − 2 2.00t 3 = −12.00t = −24.00
dt
dt
Then use sum of squares to get magnitude.
Note, numbers should have been written with units!
Q2.11
A glider is on an inclined, frictionless track. The x-axis points
downhill. At t = 0 the glider is at x = 0 and moving uphill.
After reaching the
high point of its
Glider at t = 0
High point
motion, it moves
of motion
downhill and
x=0
returns to x = 0.
x
Which of the following vx–t graphs (graphs of velocity vs.
time) best matches the motion of the glider?
vx
0
A.
vx
t
0
B.
vx
t
0
C.
vx
t
0
D.
vx
t
0
E.
t
A2.11
A glider is on an inclined, frictionless track. The x-axis points
downhill. At t = 0 the glider is at x = 0 and moving uphill.
After reaching the
high point of its
Glider at t = 0
High point
motion, it moves
of motion
downhill and
x=0
returns to x = 0.
x
Which of the following vx–t graphs (graphs of velocity vs.
time) best matches the motion of the glider?
vx
0
A.
vx
t
0
B.
vx
t
0
C.
vx
t
0
D.
vx
t
0
E.
t
In a river 100 m wide, the current flows due south at 2.0
m/s. A boat starts on the east bank with speed of 5.0 m/s
relative to the water, and a bearing due northwest.
a) How long will the boat take to cross the river?
b) What is the speed of the boat relative to the bank?
In a river 100 m wide, the current flows due south at 2.0
m/s. A boat starts on the east bank with speed of 5.0 m/s
relative to the water, and a bearing due northwest.
a) How long will the boat take to cross the river?
28 s
b) What is the speed of the boat relative to the bank?
3.9 m/s
Consider the following vectors applied to a small satellite
tethered to a space station far from Earth:
A = (1.0 N, 2.0 N, 5.0 N); B = (-4.0 N, 0. N, 7.0 N)
a) Find a force vector added to these two that would allow
the satellite to sit at equilibrium.
b) Find the angle between the two vectors.
Consider the following vectors applied to a small satellite
tethered to a space station far from Earth:
A = (1.0 N, 2.0 N, 5.0 N); B = (-4.0 N, 0. N, 7.0 N)
a) Find a force vector added to these two that would allow
the satellite to sit at equilibrium.
b) Find the angle between the two vectors.
Consider the following vectors applied to a small satellite
tethered to a space station far from Earth:
A = (1.0 N, 2.0 N, 5.0 N); B = (-4.0 N, 0. N, 7.0 N)
a) Find a force vector added to these two that would allow
the satellite to sit at equilibrium.
b) Find the angle between the two vectors.
C = −( A + B) = (3.0 N , −2.0 N , −12.0 N )
θ = cos (
−1
A⋅ B
A B
) = 46°
Starting from rest, a Team USA hockey player begins to
accelerate at time t = 0 with x, y components (5.0 m/s2, 3.0
m/s2). Find the hockey player’s velocity at the moment
when the y-component of her displacement is equal to 10.0
m.
Starting from rest, a Team USA hockey player begins to
accelerate at time t = 0 with x, y components (5.0 m/s2, 3.0
m/s2). Find the hockey player’s velocity at the moment
when the y-component of her displacement is equal to 10.0
m.
v = (13m/s, 7.8m/s)
Q3.3
The motion diagram shows an object moving along a
curved path at constant speed. At which of the points
A, C, and E does the object have zero acceleration?
A. point A only
B. point C only
C. point E only
D. points A and C
only
E. points A, C, and E
A3.3
The motion diagram shows an object moving along a
curved path at constant speed. At which of the points
A, C, and E does the object have zero acceleration?
A. point A only
B. point C only
C. point E only
D. points A and C
only
E. points A, C, and E
Q3.8
The velocity and acceleration of an object at a certain
instant are v = ( 2.0 m/s2 ) iˆ + ( 3.0 m/s ) ˆj
a = ( 0.5 m/s2 ) iˆ – ( 0.2 m/s2 ) ˆj
At this instant, the object is
A. speeding up and following a curved path.
B. speeding up and moving in a straight line.
C. slowing down and following a curved path.
D. slowing down and moving in a straight line.
E. none of these is correct
A3.8
The velocity and acceleration of an object at a certain
instant are v = ( 2.0 m/s2 ) iˆ + ( 3.0 m/s ) ˆj
a = ( 0.5 m/s2 ) iˆ – ( 0.2 m/s2 ) ˆj
At this instant, the object is
A. speeding up and following a curved path.
B. speeding up and moving in a straight line.
C. slowing down and following a curved path.
D. slowing down and moving in a straight line.
E. none of these is correct