Algebra: Solve for variable "in terms of" another variable

The formula for centripetal force, the force exerted when objects move in a circle around a center point,  is F=$\dfrac{mv^2}{r}$, where $m=$mass, $v=$velocity, and $r=$ the radius of the circle that the object is traveling.

 

1. Which of the following expresses the square of the velocity of an object moving in a circle, relative to its centripetal force, mass, and the radius of the circle it's traveling?

  1. $v^2=\dfrac{rF}{m}$
  2. $v^2={Frm}$
  3. $v^2=\dfrac{Fm}{r}$
  4. $v^2=\dfrac{rF}{mr}$

2. Which of the following expresses the mass of the object, relative to the object's centripetal force, velocity, and the radius of the circle it's traveling?

  1. $m=\dfrac{rF}{v}$
  2. $m=\dfrac{rF}{vr}$
  3. $m=\dfrac{v^2F}{r}$
  4. $m=\dfrac{rF}{v^2}$

3. Which of the following expresses the area of the circle that the object is traveling, relative to the object's centripetal force, velocity, and mass?

  1. Area=$\dfrac{mF}{v^2}$
  2. Area=$(\dfrac{mF}{v^2})^2\pi$
  3. Area=$2(\dfrac{mv^2}{F})^2\pi$
  4. Area=$(\dfrac{mv^2}{F})^2\pi$

 

 

 

An astronomy lab uses the following formula to calculate the reduced mass and diameter of Newtonian bodies. 

$\mu=\dfrac{m_1 m_2}{m_1 + m_2}d$

 

4. In the formula above $\mu$ represents reduced mass and $d$ represents diameter.  What would the formula for diameter be?

  1. $d=\mu\dfrac{m_1 m_2}{m_1 + m_2}$
  2. $d=2(\dfrac{m_1 m_2}{m_1 + m_2})$
  3. $d=\mu^2\dfrac{m_1 + m_2}{m_1 m_2}$
  4. $d=\mu\dfrac{m_1 + m_2}{m_1 m_2}$

 

 

 

A physics lab uses the following formula to measure displacement of an object ($s$). $u$ represents initial velocity.  $v$ represents final velocity. $a$ represents acceleration. $t$ represents time.

$s=ut + \dfrac{1}{2}at^2$

 

5. Which of the forumlae below represents acceleration in terms of final velocity, initial velocity, time, and displacement?

  1. $a=ut+\dfrac{1}{2}t^2-s$
  2. $a=\dfrac{ut+\dfrac{1}{2}t^2}{s}$
  3. $a=\dfrac{1}{2}\dfrac{s-ut^2}{t}$
  4. $a=\dfrac{2(s-ut)}{t^2}$

 

6. Which of the forumlae below represents initial velocity in terms of final velocity, acceleration, time, and displacement?

  1. $u=\dfrac{s}{t}-\dfrac{at}{2}$
  2. $u=\dfrac{t+\dfrac{1}{2}at^2}{s}$
  3. $u=\dfrac{s-at^2}{2t}$
  4. $u=\dfrac{at^3}{2s}$

Answer Key: