Physics 131-1 Test 1


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Questions (10 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

  1. What is the definition of systematic uncertainty?

  2. What fraction of a set of measurements should fall within one standard deviation of the mean?

  3. How would you move to produce the position versus time graph shown below? Is this reasonable?

    =8cm \epsfbox{t1af1.eps}

  4. For an object undergoing circular motion how is the velocity related to the position? What is your evidence?

  5. A student drops a tennis ball from rest while another films and analyzes the motion. The vertical position versus time plot is fitted with a quadratic function and gives $y(t) = (5.01~m/s^2)t^2 + (1.21~m/s)t + (0.7~m)$. What is the `initial velocity' in the equation? Is it consistent with the fact that the ball was dropped from rest? Explain.

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

1. 15 pts. The position of an object is described by the function

\begin{displaymath} x(t) = Bt^2 + C \end{displaymath}

where $B=3~m/s^2$ and $C=1~m$. What is the expression for the velocity in terms of $B$ and $C$? Remember that you cannot use any derivative formulas to make your calculation (only the definition of the derivative). What is the object's velocity at $t=2.0~s$?

2. 15 pts. In 1991 Mike Powell long-jumped $\rm 8.95~m$ to set a new world record. If his takeoff speed was $\rm 9.7~m/s$, then what was the farthest distance he could have jumped? Assume he jumps and lands at the same height and neglect air resistance.

3. 20 pts. A drowsy state trooper is measuring the speed of cars with a radar gun as they appear over the top of a hill. You come zooming over the hill at $\rm 80~mph$ ($36~m/s$), but the officer doesn't check your speed until two seconds have passed. Your car can decelerate at $5.0~m/s^2$, but it takes you $0.5~s$ to get your foot on the brake. Will the officer catch you if the speed limit is $\rm 65~mph$ ($29~m/s$)?

Some constants.


Acceleration of gravity ($g$) $9.8~m/s^2$