Physics 131-04 Test 1

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Questions (9 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

1. Which object is moving faster in the graph below? Which one starts ahead? What does the intersection mean?

   
   
   

   
   
   
   

2. Describe how you must move to produce a position vs. time graph with the shape shown.

   
   
   
   

3. Is it possible to actually move your body (or an object) to make vertical lines on a position vs. time graph? Why or why not? What would the velocity be for a vertical section of a position vs. time graph?

4. The picture below represents a car driving down a road. Draw velocity and acceleration vectors above the car which might represent the described motion. Also specify the sign of the velocity and the sign of the acceleration. The positive direction is toward the right. The car is moving backward. The brakes have been applied. The car is slowing down, but has not yet come to rest. Explain your reasoning.

   
   
   
   
   
   

5. The figure below shows the velocity of a particle moving on the $x$ axis. What are the initial and final directions of travel? Does the particle ever stop? Explain your reasoning.

   
   
   
   
   

Problems. Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1.

15 pts.

The astronaut orbiting the Earth in the figure is docking with the Westar VI satellite. The satellite is in an orbit 650 km above the Earth's surface where the free-fall acceleration is $a = 8.09 ~m/s^2$. The radius of the Earth is in the table below. What is the satellite's speed?

2.	20 pts.	An astronaut on a strange planet finds she can jump a maximum horizontal distance $x_1 = 20~m$ if her initial speed is $v_0 = 4~m/s$ and her launch angle is $\theta=45^\circ$ to the horizontal. What is the free-fall acceleration on this planet?
3.	20 pts.	Some cars now carry `black boxes' like those on airplanes that collect data on speed, brake status, and other information when the air bags are activated. Suppose you are a lawyer and your client was in a car accident. Your client claims he was driving at the speed limit of $v_0=15.6~m/s$ ($35~mph$) when a car came out of a driveway in front of him. He immediately slammed on the brakes which decelerate the car at a rate $\vert\vec a\vert = 8~m/s^2$. From the investigation you know your client hit the brakes at a point $22~m$ from the crash. The `black box' recorded a speed $v_1 = 2~m/s$ at the moment of impact when the airbag opened. Is he lying?

Physics 131-04 Constants

Speed of Light ($c$)	$2.9979\times 10^8~m/s$	proton/neutron mass	$1.67\times 10^{-27}~kg$
$R$	$8.31J/K-mole$	$g$	$9.8~m/s^2$
Gravitation constant	$6.67 \times 10^{-11}~N-m^2/kg^2$	Earth's radius	$6.37\times 10^6~m$
Earth-Moon distance	$3.84\times 10^8~m$	Electron mass	$9.11\times 10^{-31}~kg$

Physics 131-04 Equations

$$\Delta x = x_{finish} - x_{start} \qquad \Delta \vec r = \ve... ...{start} \quad \Delta \vec v = \vec v_{finish} - \vec v_{start}$$

$$\bar v = \langle v \rangle = {\Delta x \over \Delta t} \quad... ...\to 0} {x (t+\Delta t) - x(t) \over \Delta t} = {dx \over dt}$$

$$\bar a = \langle a \rangle = {\Delta v \over \Delta t} \quad... ... \to 0} {v(t+\Delta t) - v(t) \over \Delta t} = {dv \over dt}$$

$$x = {1 \over 2}at^2 + v_0t + x_0 \qquad v = at + v_0 \qquad a_g = -g$$

$$\vec A = A_x \hat i + A_y \hat j + A_z \hat k \quad \vec A +... ... B = (A_x + B_x)\hat i + (A_y + B_y)\hat i + (A_z + B_z)\hat i$$

$$a_c = {v^2 \over r} \qquad \vec v \perp \vec r \qquad \vec v \perp \vec a_c$$

$$\vec v = {d \vec r \over dt} = {dx \over dt}\hat i + {dy \... ...over dt}\hat i + {dv_y \over dt}\hat j + {dv_z \over dt}\hat k$$

$$\theta = {s \over r}\quad \sin \theta = {opp \over hyp} \qua... ...uad \cos^2\theta + \sin^2\theta =1 \quad x^2 + y^2 + z^2 = R^2$$

$$x = {-b \pm \sqrt{b^2 -4ac} \over 2a} \quad {\rm C} = 2 \pi ... ... {\rm Area} = {1 \over 2}bh \quad {\rm Area} = 4 \pi r^2 \quad$$

$${\rm Volume} = {4 \over 3} \pi r^3 \qquad {\rm Volume} = \pi r^2 l \qquad$$