Toy car W travels across a horizontal surface with an acceleration of $ a_w $ after starting from rest. Toy car Z travels across the same surface toward car W with an acceleration of $ a_z $, after starting from rest. Car W is separated from car Z by a distance $ d $. Which of the following pairs of equations could be used to determine the location on the horizontal surface where the two cars will meet, and why?

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Toy car W travels across a horizontal surface with an acceleration of $ a_w $ after starting from rest. Toy car Z travels across the same surface toward car W with an acceleration of $ a_z $, after starting from rest. Car W is separated from car Z by a distance $ d $. Which of the following pairs of equations could be used to determine the location on the horizontal surface where the two cars will meet, and why?(a) $x = x_0 + v_{0}t + \frac{1}{2}a_wt^2$ for car W, and $x = x_0 + v_{0}t + \frac{1}{2}a_zt^2$ for car Z. Since the cars will meet at the same time, solving for $t$ in one equation and placing the new expression for $t$ into the other equation will eliminate all unknown variables except $x$.
, (b)

$x = x_0 + v_{0}t + \frac{1}{2}a_wt^2$ for car W, and $\Delta x = x &#8211; x_0$ for car Z. Since the separation distance is known between both cars, the displacement for car Z can be used in the equation for car W so that the time at which the cars meet can be determined. Once known, the time can be used to determine the meeting location.

, (c) $\Delta x = x &#8211; x_0$ for car W, and $x = x_0 + v_{0}t + \frac{1}{2}a_zt^2$ for car Z. Since the separation distance is known between both cars, the displacement for car W can be used in the equation for car Z so that the time at which the cars meet can be determined. Once known, the time can be used to determine the meeting location.
, (d) $\Delta x = x &#8211; x_0$ for car W, and $\Delta x = x &#8211; x_0$ for car Z. Since the location at which the cars meet represents the final position of both cars, the separation distance for both cars can be substituted into both equations to determine the final position of both cars.
, (e) None of the choices.
:

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