Aim  How are changes in velocity calculated?
C. Acceleration – changes in an objects velocity
1. a avg = change in velocity/change in time (show vf – vi/ tf –ti)
2. units are m/s over s = m/s2
3. acceleration can be positive or negative (slow down is negative)
give problem 5 from workbook
HW Read in text pages 48-58 and answer questions page 49 3-5 and 1-3 on p 53
D. Kinematics Equations
1. a = v/t
2. vf = vi + at
3. d = vi t + ½ at2
4. vf 2 = vi2 + 2ad
5. Go over what each term means
6. An object starts from rest (initial velocity), an objects brakes to a stop (final v)
.
Practice Problems (workbook page 12)
P49 #1 As a bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at
–4.1 m/s2 as it slows from 9.0 m/s to 0 m/s. find the time interval of acceleration for the
bus.
v/t
A=
-4.1 m/s2 = 9 m/s / t
2.2 seconds
P49 #2 A car traveling at 7 m/s
#5) A car accelerates from rest at -3 m/s2. (a) What is the velocity at the end of 5.0 s? (b)
What is the displacement after 5.0 sec
a = vf-vi/t
vf = -15 m/s2
b)
v=d/t d= - 45m
#6) A ball initially at rest rolls down a hill with an acceleration of 3.3 m/s2. If it
accelerates for 7.5 s, how far does it travel?
D=vi t + ½ at2
d=93 m
#7) A jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum
rate of -5.0 m/s2 as it comes to rest on the landing strip. Can this plane land at an airport
where the runway is 0.80 km long?
vf 2 = vi2 + 2ad d=1000 meters can not land
#8) The Easter Bunny and the Tooth Fairy are running a race together. They start from
rest and accelerate at 5 m/s2 for 10 seconds. The Easter bunny then has a heart attack
(too much chocolate) and falls over. The tooth fairy stops accelerating at this point and
he maintains his speed at a constant rate until he finishes the race 20 seconds later.
(a) What is the total distance traveled by the tooth fairy?
d = vi t + ½ at2
= 250 meters
vf = vi + at = 50 m/s for vf
v=d/t d=1000m
dt = d1 + d2
(b) What is the Easter Bunny's average velocity while he was running?
V=d/t 250m/10s
= 25 m/s
(c) What is the tooth fairy's average velocity for the whole trip?
V=d/t 1250m/30s = 42m/s
#9) The school bully stuffs you in an oil barrel and kicks it. You roll on a horizontal
surface with an initial velocity of 20 m/s. You slow down at a rate of 2 m/s2 for 5
seconds until you reach a hill (note you are slowing so the acceleration would be
negative). At this point you roll down a hill and accelerate at 3.5 m/s2 down the hill for
10 seconds. What is the total distance you traveled on your mystical journey and what
final speed do you achieve at the base of the hill.
vf = vi + at = 10 m/s
distance along the first part of the trip
d = vi t + ½ at2
75 meters (negative a)
d = vi t + ½ at2
100+ ½ -2 25
10 *10 + ½ (3.5) (100) = 100+175 =275 m
total distance = 75+275= 350m
vf 2 = vi2 + 2ad
= 100 + (2)(3.5)(275) = 2025 square root = 45 m/s2