Worksheet 1: Math review and 1D motion
1
Sig Figs and Scientific Notation
1.1
How many significant figures does each of the following numbers have?
3
e. 0.062
i. 1.062
b. 62.1
f. 0.620
j. 6.21 × 103
c. 6210
g. 0.62
k. 6.21 × 10−3
d. 6210.0
h. .62
l. 62.1 × 103
a. 6.21
1.2
Compute the following numbers with the correct number of sig figs:
a. 33.3 × 25.4 =
846
d. 2.345 × 3.321 =
b. 33.3 − 25.4 =
e. (4.32 × 1.23) − 5.1 =
c. 33.3 ÷ 45.1 =
f. 33.32 =
1.3
Express the following numbers and computed results in scientific notation
a. 9,827
9.827 × 103
d. 32, 041 × 47 =
b. 0.0000000550
e. 0.059 ÷ 2, 304 =
c. 3,200,000
f. 320. × 0.050 =
2
Algebra Review:
2.1
a.
Simplify or solve each:
102
(103 )2
10−4
b.
(102 )9
(102 )10
c.
(102 )10
1020
d.
109
(104 )2
e. Solve for a: y = v0 t + 21 at2
2.2
f. Solve for g: T = 2π
q
L
g
g. Solve for µ :mv2 r=µmg
Solving systems of equations
1
A) h = h0 + v0 t − gt2 ,
2
B)v 2 = v02 − 2gh,
C)v = v0 − gt
1) You are given v0 , h0 , and g and the equations above. Do you have enough equations to solve for
v? Can you do it with two equations? With one? Solve for v:
2) You are given v, t, and g. Do you have enough equations to solve for h? Can you do it with two
equations? With one? Solve for h:
3
3.1
SI Units and Dimensional analysis:
Convert the following to SI units. Work across the line and show all steps in the
conversion. Use scientific notation and apply the proper use of significant figures.
a. 9.12 µs ×
b. 3.42 km ×
c. 44 cm/ms ×
d. 80 km/hr ×
e. 8 in ×
f. 13 in2 ×
g. 250 cm3 ×
1s
106 µs
= 9.12 ×10−6s
3.2
Determine which of the following statements are reasonable:
a. Joe is 180 cm tall.
1.80 m ≈ 6 ft tall, which is reasonable
b. I rode my bike to campus at a speed of 50 m/s
c. A skier reaches the bottom of the hill going 25 m/s
d. I can throw a ball a distance of 2 km
e. I can throw a ball at a speed of 50 km/hr
3.3
Use the following dimensions for variables to determine which equations are valid:
[x] = [L],
[m] = [M ],
[E] = [M ][L]2 /[T ]2 ,
x = vt
x = 21 at2
v 2 = x + ax
v = at
F = ma
E = Fx
E = 12 p2 x
[v] = [L]/[T ],
[F ] = [M ][L]/[T ]2 ,
[L]
[L]= [T
] · [T ] = [L],
[t] = [T ],
[a] = [L]/[T ]2 ,
[p] = [M ][L]/[T ],
which is valid
[A] = [L]2 ,
[P ] = [M ][L]3 /[T ]2
Reading graphs
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4
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1. During what time interval is there acceleration?
2. During what time interval is there zero velocity?
3. At what instant is velocity zero but acceleration nonzero?
4. During what time interval is there the highest speed?
5. During what time interval is there slow down?
6. During what time interval is there speeding up?
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7. Do your best to sketch graphs for velocity and acceleration
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x
√
13
θ
x
θ = 33◦
|A| =
y
θ=
|B| =
x
y
◦
Ax = 5 cos(60◦ ) = 5/2
√
Ax = 5 sin(60◦ ) = 5 3/2
x
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A
30
30◦
y
Ax =
◦
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Ax =
x
Ax =
30◦
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A
Ax =
y
θ=
|C| =
30◦
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Cx = 0, Cy = −3
y
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Bx = −4, By = 4
x
Ax = 3, Ay = −2
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x
y
Ax =
Ax =
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x
30◦
θ=
|D| =
Dx = −3, Dy = −4
x