Unit 2, Day #1, Accel
What are the 5 key equations that we have learned thus far?
a) ____________________________
b) ____________________________
c) ____________________________
d) ____________________________
e) ____________________________
What are the 4 “NEW” equations of motion?
a) ____________________________
b) ____________________________
c) ____________________________
d) ____________________________
*
*
These can only be used when the __________________________ is constant
v
v2
v1
t1
t2
t1
t2
t
v
v2
v1
t
Examples:
1) Jimmy is at rest in his corvette. Suddenly he hits the
gas and accelerates at a constant rate of 4 m/s2. What will his velocity be after 5 seconds?
2) A plane is moving at a speed of 50 mph when it lands on a runway. Accelerating
uniformly, it comes to a stop after covering a quarter mile. How long did it take to stop?
What was its acceleration?
3) A race car travelling at 60 mph accelerates uniformly to a speed of 90 mph, covering 50
meters in the process. What was the car’s acceleration?
Derivations of the equations
v
v2
v1
t1
t2
t1
t2
t
v
v2
v1
t
Unit 2, Day #2, Accel
The 5-Step Approach to Problem Solving
1) _______________________________________________________________
2) _______________________________________________________________
3) _______________________________________________________________
4) _______________________________________________________________
5) _______________________________________________________________
Examples
1. A car is cruising at 100 km/h when it slams on the breaks. It stops in 4.5 seconds. If the
acceleration is constant, find the acceleration and the distance it took to stop the car.
2. A bird is flying in a straight line with a uniform velocity of 8 m/s. It begins a constant
acceleration of 2 m/s2 in order to catch up to another bird. How long would it take the bird to fly
100 m?
3. Two lines are painted onto a road, 50 meters apart. The car crosses the 1st line at a speed of 40
m/s, and then crosses the 2nd line with a speed of 20 m/s. Assuming a constant acceleration
along the way, find the acceleration of the car and the time spent between the lines.
4. A race car, starting from rest, accelerates from 0 to 60 (mph of course) in 3.5 seconds. If the
acceleration is constant, find the distance that the car travels in each of the first two (2) seconds.
Unit 2, Day #3, Accel
Free-Fall
The basic “assumptions” of free-fall ________________
The free-fall equations:
______________
________________
__________________________  ______________________
__________________________  ______________________
__________________________  ______________________
In-Class Examples
A sky diver falls off a 200m high cliff. He doesn’t jump, but simply falls.
1.
Assuming that we neglect air resistance, how fast will the man be traveling
after falling for 20 m?
2.
If his parachute never opened, how long would it take him to hit the ground?
3.
How far would the parachutist fall during the 3rd full second that he dropped?
4.
If all objects accelerate at the same rate when falling near the earth’s surface,
why do some objects actually hit the ground faster than others (assuming that
they are dropped at the same time from the same height)?
5.
Sketch the y-t and v-t graphs of an object that
is in free fall.
U2, Day #3 Homework (ACCEL)
Basic Equations (including Free-fall) Worksheet
1. A car starting from rest on a straight road increases its speed to 20 m/sec in 25 seconds.
What is the car’s acceleration? How far did it move?
2. A car starting from rest is accelerating at a constant rate of 3 m/sec2. What is its speed
after 11.5 seconds?
3. A bus moving at 20 m/sec is accelerated at the rate of 0.5 m/sec2. What is the speed of
the bus after 6 seconds? How far does it travel?
4. A coin is dropped from the roof of a building. If the coin takes 5 seconds to reach the
ground, how tall is the building?
5. After starting from rest, a ball rolls down an incline 12 m long in 3 seconds. At what
rate is the ball accelerated?
6.
Bob Feller pitched a baseball that traveled from the pitcher’s mound to homeplate
(60 ft., 6 inches away) in 0.419 seconds. Assuming a constant speed from pitcher to
catcher, what was the ball’s average speed in ft/sec? In mi/hr? If the catcher allowed
his mitt to recoil backward 0.25 ft, what is the acceleration of the ball while slowing?
7. A book is held in the air 7.0 cm above a table top and then released. How long will
the book be in the air?
8. Lt. Colonel John L. Stapp achieved a speed of 632 mph (284 m/sec) in a rocket sled at
the Holloman Air Base Development Center, Alamogordo, New Mexico, on March
19, 1954. Running on rails powered by 9 rockets, the sled reached its top speed in 5
seconds. Find the average acceleration in reaching top speed. How far did the sled
travel in reaching top speed?
9. A spacecraft increases its speed at the rate of 0.20 mi/sec2. How much time is required
for the speed to increase from 7 mi/sec to 8 mi/sec?
Answers
1.
a = 0.8 m/s2
d = 250 m
6.
Vav = 144.4 ft/sec = 98 mi/hr
a =  41,500 ft/s2
2.
VF = 34.5 m/s
7.
0.12 sec
3.
VF = 23 m/s
d = 129 m
8.
a = 57 m/s2
d = 710 m
4.
122.5 m high
(you should get  122.5 m)
9.
t = 5 sec
5.
a = 2.6 m/s2
Unit 2, Day #4, Accel
Throw ups
The basic assumptions:
a) __________________
b) __________________
c) __________________
A man throws a ball straight upward. The ball
leaves his hand at a height of 1 m above the
ground and its initial velocity is 20 m/s.
#1
a) How high above the ground will the ball reach?
b) How long will the ball take to reach its maximum
height?
c) When will the ball be 11 m above the ground?
Throw-up / Come Downs
The basic assumptions:
a) __________________
b) __________________
____________
c) __________________
____________
#2
A man throws a ball straight upward. It reaches a maximum height of 30 m and then falls
back down. Find:
a)
b)
c)
d)
The velocity at which the ball was thrown.
The time taken to catch the ball again (at the same height from which it was thrown)
The velocity at which the ball lands in the man’s hand.
The impact velocity of the ball if the man misses it and it falls 1 extra meter and
hits the ground.
#3
A man launches a popcorn ball straight up into the air. It reaches its peak, and then
begins to fall back to the ground. 4 seconds after it was released from the man’s hand, a
bird catches the ball 20 ft above the ground. What was the velocity at which the ball left
the man’s hand?
U2, Day #4 Homework (ACCEL)
Throw-ups and Throw-downs Worksheet
1) A ball is thrown upward with an initial velocity of 20 m/s. How high will it
go? How long will it take to reach this maximum height?
2) An object is launched from ground level into the air. It reaches a maximum
height of 52 ft.
a) How long does it take to reach its peak.
b) What was the initial velocity with which it was thrown upward?
c) What velocity will it strike the ground with on its way downward?
d) What will be its total flight time (from launch to land)
3) A rock is dropped off a 50m high cliff. Find:
a) the time it takes for the rock to hit the ground.
b) the velocity with which the rock strikes the ground.
c) the reason why the size, shape, weight, etc of the rock doesn’t affect the
answers to parts ‘a’ and ‘b’. What must be “neglected”.
4) How far will an object in free-fall drop during the 4th full second of its free
fall? `
5) New type of problem: “Throw Down”  ………A man stands on a cliff and
throws a rock downward with an initial speed of 10 m/s. The rock hits the
ground 5 seconds later. How high is the cliff?
6) An object is launched straight up into the air. It lands 8 seconds later at the
bottom of a 5 ft deep hole that is next to the launching site. Find the maximum
height (above the launching site) reached by the object.
Answers:
1) 20.41 m; 2.04 sec
2) 1.8 sec; 57.87 ft/s; -57.87 ft/s; 3.60 sec
3) 3.19 sec; -31.3 m/s; since air resistance is neglected, ALL objects fall at the same rate near the earth’s
surface.
4) 34.4 m
5) 172.5 m
6) 255.1 m
Unit 2, Day #5, Accel
Chase Problems:
What is a chase problem? It’s a scenario where two objects are involved, and they have
the same position at some later time. They could either ….
a) ______________________________________________
b) ______________________________________________
c) ______________________________________________
d) ______________________________________________
e) ______________________________________________
The key equation(s): _______________________
_______________________
Two relationships that you need to look at: ______________ or _______________
In-Class Examples:
1) Timmy is running at a constant speed of 6 m/s. He sees Susie running 50 m in front of
him. She is moving at a constant speed of 4 m/s, in the same direction. How long will it
take for Timmy to catch Susie?
2) As a continuation of the last problem, Timmy passes Susie, running at his constant
speed of 6 m/s. Susie decides to pick up the pace, very gradually. She begins to
accelerate at a constant rate of 0.1 m/s2. How long will it take her to catch Timmy?
3) A man drops a penny off the top of a 100 ft tall building. Exactly 1 second later, another
man throws a nickel downward from the same place as the first man. What is the
minimum speed that the nickel must be thrown at in order to catch the penny?
4) In a strange, yet exciting, crash-test-dummy crash, two cars start by facing each other
1000m apart on a straight road. The first car accelerates form rest with a constant
acceleration of 4m/s2. The second car accelerates at a rate of 8 m/s2 for 5 seconds but then
settles into a constant speed. Find the elapsed time before these two cars collide
U2, Day #5 Homework (ACCEL)
Chase Problems Worksheet
1. A man and a woman stand facing each other. They are 100 m apart. They start
at the same time and move towards each other (in a straight line) with a
constant acceleration. If they meet 10 seconds later and if the woman’s
acceleration is twice that of the man’s, find their accelerations.
2. Superman is standing at a train station. Joker passes on a train that is traveling
at a constant speed of 50 mph along a straight track. As soon as the train passes
the station, Superman begins to chase it, accelerating at a constant rate of 4
ft/s2. How long will it take Superman to catch the train?
3. A hyena spots a rabbit 50 m in front of him in a field. Both animals start
running at the same time, with the hyena in pursuit of the rabbit (both heading
in a straight line). Unfortunately for the rabbit, the hyena accelerates one and a
half times faster than it does. If the rabbit accelerates at a constant 2 m/s2, find
the time necessary for the hyena to catch the rabbit. Solve by using the
equations of motion.
4. A man drops a penny off the top of a 100 ft tall cliff. Another man, lying on the
ground below the cliff, throws another penny straight up at with an initial
velocity of 50 ft/s. Find the time at which both penny’s are at the same height
above the ground. At this time, how high above the ground will they be.
5. A new car gives an older car a “running” head-start. The old car starts out with
and maintains a velocity of 18 m/s. The new car starts from rest and
accelerates at a constant rate of 2 m/s2 until it reaches a constant velocity of 26
m/s. It then drives at a constant speed. How long will it take for the new car to
catch the old car? Solve by using the equations of motion.
Answers:
1) man: .67 m/s2 woman: 1.34 m/s2
2) 37sec
3) 10 sec
4) 2 sec; 35.6 ft above the ground (64.4 ft below the cliff)
5) 21.125 sec
Unit 2, Day #6, Accel
In-Class Examples
1) A smart-aleck kid walking across the Tacony-Palmyra Bridge stops in the middle of the
bridge and spits into the beautiful waters of the Delaware. Not really a spit, but more of a
drool. The saliva literally “falls” off his lip. If it takes the spit 5.5 seconds to hit the water,
how high is the bridge? How accurate do you think this measurement is? What would
affect the measurement?
2) Rabbit/Hyena Problem …. Revisited! A hyena spots a rabbit 50 m in front of him in a
field. The hyena gives the rabbit a 5 second headstart, and then starts running after the
rabbit (both heading in a straight line). The hyena still accelerates at 3 m/s2 and the rabbit
still accelerates at 2 m/s2. Find the time necessary for the hyena to catch the rabbit. Solve
by using the equations of motion.
3) The Road Runner, traveling at 55 meters per second, is cruising down the road, Wili E.
Coyote sees our fine-feathered friend and starts out from rest to catch him just as the road
runner passes him. In 10 seconds, he reaches for the Runner (just before he smashes into a
rock.) What was his acceleration?
4) Atom Ant is traveling with an initial velocity of 20 cm/sec. He begins to accelerate at a
rate of 8 cm/sec2 for 5 seconds. What is his total displacement? What is his displacement
in the last second?
5) Joe Citizen is cruising in his car toward a green light at 20 m/sec. At 36 meters from the
intersection, he jams on his brakes. (There is an obstruction in the intersection. Why
it’s . . . THE BATMOBILE, stopped to help some poor pedestrian in trouble!) If Joe can
slow down at  6 meters per second 2 , how long will it take him to stop? How far does he
travel in this time? Has the Batmobile seen better days?
6) A baseball is thrown vertically downward with an initial speed of 20 meters per second
from a tower 150 meters high. How long does it take to hit the ground? How fast is it
going when it hits?
Answers
1) 148 m
4) 200 cm; 56 cm
2) 30.81 sec
5) 3.33 sec; 33.3 m
3) 550 cm; 11 m/s2
6) 3.85 sec;  57.8 m/s
U2, Day #6 Homework (ACCEL)
Free Fall, Throw Ups, Up & Downs, and Chase Problems
1. A rock is dropped off a 50m high cliff. Find:
a) the time it takes for the rock to hit the ground.
b) the velocity with which the rock strikes the ground.
c) the reason why the size, shape, weight, etc of the rock doesn’t affect the
answers to parts ‘a’ and ‘b’. What must be “neglected”.
2. How far will an object in free-fall drop during the 4th full second of its free fall?
During 20th full second?
3. A “whimpy” Nerf rocket is launched straight up into the air from ground level. Its
initial velocity is 10 m/s. Find:
a) the maximum height that it can attain.
b) the time taken to reach it apex.
c) the full flight time if it drops straight down.
d) the time(s) when the rocket is 5 m above the ground.
4. A boy throws a ball straight up from 4 ft above the ground. The ball reaches a max
height of 30 ft. Find
a) the ball’s initial velocity.
b) the total flight time of the ball if it then proceeds to land on the ground (since
the boy misses catching it).
5. A new car gives an older car a “running” head-start. The old car starts out with and
maintains a velocity of 13 m/s. The new car starts from rest and accelerates uniformly.
40 seconds later, the new car reaches its maximum speed and pursues the older car
with a uniform velocity of 21 m/s. How long will it take for the new car to catch the
old car? Solve by using the equations of motion. Then, try the graphical approach.
(NOTE: For all problems, use a = -9.8 m/s2 = -32.2 ft/s2)
Answers
1) 3.19 sec; -31.3 m/s; ______
2) 34.3 m; 191.1 m
3) 5.1 m; 1.02 sec; 2.04 sec; 0.876 sec; 1.165 sec
4) 22.57 m/s up; 2.30 + 2.47 = 4.77 sec
5) 52.5 sec
U2, Day #7 Homework (ACCEL)
Kinematics Review Sheet
(m/s/s is same as m/s2)
1. A car is moving at 20 m/s and accelerates to 35 m/s in 100 meters. (a) What was the cars
acceleration? (b) How much time did it take to accelerate?
2. A hockey puck is sliding on ice and accelerates to a rest at 0.04 m/s/s from a velocity of 22 m/s.
(a) How far did the puck slide? (b) How much time did it take to come to a rest?
3. An airplane prepares to land on a runway. The plane touches down at 80 m/s. With what
acceleration must the plane have in order to stop in time on the 1000-meter runway?
4. A sprinter is able to accelerate from rest to a velocity of 11.4 m/s over a distance of 16 meters.
What is the sprinters acceleration? What will the time for the sprinter be if she can hold this
velocity for the rest of the 100 meters? (total time)
5. An aircraft carrier launch consists of throwing a plane off of its deck at 36 m/s. The plane is
pulled by a cable for a distance of 40 meters. (a) Determine the acceleration of the aircraft. (b)
How much time does it take to accelerate? (c) How many “g’s” is this on the pilot? (how many
9.8’s fit into it)
6. A boy drops a 20 gram stone into a quarry from a tall cliff. He times the fall of the stone and
measures 1.6 seconds. (a) Determine the height of the cliff. (b) Determine the impact velocity
of the stone as it hits the water.
7. A ball is thrown upwards off of a 30-meter tall building. It passes by the rooftop and hits the
ground at 30 m/s. (a) Determine the time in the air (b) Determine the initial velocity of the ball
(c) How high did the ball reach from the ground?
8. An observer watches a flowerpot as if falls along side of a building. He notices that it passes his
friends window (which is 18 meters from the ground) and takes 0.76 seconds to reach the
ground. (a) At what speed does the pot hit the ground? (b) If the pot fell from rest, what height
did it start from with respect to the ground? (c) At what speed did it pass his friends window?
9. A car accelerates form rest to a velocity of 36 m/s in 4 seconds. It then coasts for 540 meters. It
then comes to a rest at a rate of 12 m/s/s. (a) sketch the V/T graph and determine its total
displacement (b) Determine its acceleration in the beginning and end (c) find the time to come
to a rest.
10. A hot wheel is shot out of “The House of Terror” launching platform with a velocity of 3.8 m/s
from rest. The house of terror takes 0.2 seconds to launch the car. Due to friction on the track,
it immediately begins to slow up to a rest over a distance of 12 meters of track. (a) Sketch the
V/T graph (b) Determine the acceleration and deceleration of the hot wheel car. (c) find the
color of the hot wheel.
11. Car A is at rest in an intersection when car B passes by it at 30 m/s and whips an egg. After car
A is plastered by the egg and takes a total of 5 seconds to wipe it off of the windshield, it begins
to chase car B. It catches B in 12.2 seconds. At what rate did car accelerate from rest in order
to catch car B?
12. A woman walks down onto a train platform and notices her train has already left. She is
moving with a speed of 8 m/s when she begins to chase after it. The train is 30 meters ahead of
her, moving with an initial speed of 4 m/s and accelerating at 2.1 m/s/s. Does she catch the
train? Explain with quantitative information. IF she catches the train, how long did it take to
catch it (time and distance).