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PHYS 407S

Ver. B

Midterm Exam 1

September 28, 2017

Name:

• Time for the exam: 7:10pm – 9:00pm.

• Closed book, closed notes, closed neighbor. Calculators are allowed.

• The exam has five numbered physics problems. Please complete any four problems. Cross out

the problem you do not wish to be graded on this cover page page. If there is any ambiguity, we

will grade the first four problems (no exceptions).

• Show your work. An unjustified answer may receive little or no credit.

• Derive your solution in terms of variables first (analytical) before you plug in numbers (numerical).

• Your test must be neat and legible. We will take off points for sloppiness and missing units.

Problem Points Points

Possible Made

1 25

2 25

3 25

4 25

5 25

Total 100

1

PHYS 407S

Units and Conversions

quantity SI unit selected conversions

length meter (m) 1 ft = 12 in = 0.3048 m

1 in = 2.54 cm

1 yard = 3 ft

1 mile = 1760 yards = 1609 m

mass kilogram (kg) 1 lb = 16 oz = 0.453 kg

volume cubic meter (m3) 1 gallon = 4 quarts = 3.79 l

1 l (liter) = 1000 cm3 = 10−3 m3

symbol prefix value

µ micro 10−6

m milli 10−3

c centi 10−2

d deci 10−1

k kilo 103

M mega 106

G giga 109

Kinematics

velocity: ~vavg = ∆~x∆t ; ~v = ~˙x =

d~x

dt

acceleration: ~aavg = ∆~v∆t ; ~a = ~˙v =

d~v

dt = ~¨x =

d2~x

dt2

free-fall on Earth: constant acceleration ~a = −gjˆ, g = 9.8m/s2 (straight down)

if acceleration is constant, a(t) = a = const, then: v(t) = at+ v0, x(t) = 12at

2 + v0t+ x0

centripetal acceleration ac = v2/r

Derivatives

d

dx

xn = nxn−1 ,

d

dx

(f(x) + g(x)) =

df

dx

+

dg

dx

,

d

dx

(Cf(x)) = C

df

dx

Integrals ∫

xn dx =

1

n+ 1

xn+1 + const ,∫

(f(x) + g(x))dx =

∫

f(x) dx +

∫

g(x) dx+ const ,

∫

Cf(x) dx = C

∫

f(x) dx+ const∫ xf

xi

f(x) dx = F (xf )− F (xi),where F (x) is an anti-derivative to f(x).

Trigonometry

SOHCAHTOA, Pythagorean Theorem c2 = a2 + b2

sin(α+ β) = sinα cosβ + sinβ cosα, cos(α+ β) = cosα cosβ − sinα sinβ

Quadratic Equation

The equation ax2 + bx+ c = 0, has solutions x = −b±

√

b2−4ac

2a .

2

PHYS 407S

1. (25 pts) To try to win the $25 first place prize in South Park’s annual sled competition, Cartman

has constructed a $15,000 rocket sled. He is doing a test run down Main Street to see how well

it works. As the rocket engine fires and he sleds towards downtown, the sled has a constant

acceleration for 10.0 seconds until the engine shuts off. At that moment, a parachute deploys,

which begins slowing the sled at a rate of 4.0 m/s2. Exactly 15.0 seconds after the rocket sled

started moving, Cartman passes in front of the City Wok restaurant, 950 meters from his starting

point.

(a) (15 pts) What was the acceleration of the rocket sled for the first 10 seconds, while the engine

was on? (Hint: it may be helpful to draw a plot or two.)

(b) (10 pts) Cartman is unaware that Officer BarBrady is outside City Wok, measuring the speed

of cars passing by, just as they pass in front of City Wok. The speed limit by the restaurant

is 45 mph. The penalty for speeding is $50 for every 5 mph over the speed...

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