PHYSICS
REVIEW SHEET
9-WEEK EXAM
Concepts And Definitions
Definitions of fact, hypothesis, law, theory
Explain the scientific method
Difference between average and instantaneous speed and speed and velocity
D vs. T and V vs. T graphs
Describe Acceleration and Free Fall
Distinguish between scalars and vectors
Horizontal projectiles
Shots at an angle
Add and resolve vectors into their components
Sample Problems
1. You want to complete a 500 mile trip in 10 hours. Yet, because of the ever-present construction zones, you only
average 40 mph for the first two hours. You then need to stop for lunch, which kills another 1/2 hour.
How fast must you drive (on average) to complete the trip on time?
DATA
EQUATIONS
MATH
ANSWER
d1 = 40 (2) = 80 miles
dt = 500 miles
tt = 10 hrs
v1 = 40 mph
t1 = 2 hrs
t2 = 0.5 hrs
v2 = 0 mph
d2 = 0 miles
v3 = d3 / t3
d3 = dt – d1 – d2
d3 = 500 – 80 – 0 = 420
miles
t3 = tt – t1 – t2
t3 = 10 – 2 – 0.5 = 7.5 hrs
d1 = v1 (t1)
v3 = 420 / 7.5
56 mph
2. If an airplane can go from its top speed of 48 m/s to a taxi speed of 5.5 m/s in 8.37 seconds, how long a runway
does it need?
DATA
EQUATIONS
MATH
ANSWER
vi = 48 m/s
d = vit + ½ at2
vf = 5.5 m/s
a = (vf- vi) / t
t = 8.37 seconds
a = (5.5 – 48) / 8.37 = - 5.08 m/s2
d = 48(8.37) + ½ (-5.08)(8.37)2
224 m
3. How fast is a rock moving as it strikes the pavement if it is dropped from the top of a building that is 223 meters
tall?
DATA
EQUATIONS
MATH
ANSWER
vi = 0
vv = gt
dv = 223 m
2𝑑𝑣
𝑡= �
𝑔
2(223)
𝑡= �
9.81
= 6.74 seconds
66.1 m/s
vv = 9.81 (6.74)
Distance v Time
60
50
40
30
20
10
0
0
10
20
30
Time (in min)
4. When is the car stopped? _0-4 min and 28-32 min__
5. When is the car speeding up? _32-42 min___
6. When is the car slowing down? _at 16 min and at 28min _______
7. When is the car traveling at its fastest constant speed? _4-16 min____
8. How far did the car travel in the first 15 minutes? _33 m___ (it doesn’t start at d = 0)
9. How fast is the car traveling at t = 15 minutes? __3m/min___ (slope of the line)
10. When is the car furthest from the observer? __28-32 min___
11. When does the car pass the observer? __at 42 min__
12. How far is the car from the observer at t = 40 minutes? _24 m___
13. How fast is the car traveling at t = 30 minutes? _0 m/min___
40
Velocity vs Time
20
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
50
60
Time (in seconds
14. When is the car not moving? __36-39 sec___
15. When is the car moving at its fastest speed? __0-12 seconds___
16. How fast is the car traveling at t = 10 seconds? __13 m/s__
17. How far does the car travel in the first ten seconds? ___65 m___
18. When is the car speeding up? _0-24 and 39-54 sec__
19. When is the car slowing down? _30-36 sec__
20. When is the car gaining speed at the highest rate? __0-12 sec___
21. What is the acceleration of the car at t = 56 seconds? __0____
22. What is the acceleration of the car at t = 20 seconds? __0.333 m/s2___
23. What is the acceleration of the car at t = 32 seconds? __-3.33 m/s2___
24. How far does the car travel in the first minute? __567 m__
25. A motorboat heads due east at 12.0 m/s across a river that flows towards the south with a current of 3.50 m/s.
A. What is the resultant velocity of the boat?
DIAGRAM
MATH
ANSWER
Vr = 𝑣𝑅 = √122 + 3.52 = 12.5
𝜃 = tan−1
3.5
= 16.2°
12
12.5 m/s
@
16.2̊ S of E
Or
73.8̊ E of S
Or
106̊
B. If the river is 1360 m wide, how long does it take the boat to cross?
DATA
EQUATIONS
MATH
ANSWER
d = 1360 m
t=d÷v
t = 1360 ÷ 12
v = 12 m/s
113 seconds
C. How far downstream is the boat when it reaches the other side?
DATA
EQUATIONS
MATH
ANSWER
v = 3.5 m/s
d = vt
d = 3.5 (113)
t = 113 sech
395.5 m
27. A cannon is shot horizontally at a speed of 150 m/s off of a cliff 45 meters high. How far away from the base of
the cliff will the cannonball land?
DATA
EQUATIONS
MATH
ANSWER
vh = 150 m/s
d = vht
dv = 45 m
𝑡= �
2𝑑𝑣
𝑔
2(45)
𝑡 = � 9.81 = 3.03 seconds
dh = 150 (3.03)
454.5 m
28. If a shell is fired from a cannon with a velocity of 20 m/s at an angle of 30°, how far will the shell travel away
from the cannon?
DIAGRAM
MATH
ANSWER
vv = 20(sin 30) = 10 m/s
vh = 20(cos 30) = 17.3 m/s
tt = 2tup = 2(10) ÷ 9.81 =
2.04 s
dh = 17.3 (2.04)
35.3 m