Q7DQ - University Physics with Modern Physics

Question

When a Dodge Viper is at Elwood’s Car Wash, a BMW Z3 is at Elm and Main. Later, when the Dodge reaches Elm and Main, the BMW reaches Elwood’s Car Wash. How are the cars’ average velocities between these two times related?

Step-by-Step Solution

Answer

The relation between the average velocities of two cars is as$v_1=-v_{2-1}$, which means equal and opposite.

Step 1: Average velocity

Average velocity refers to the object's speed by which is moving is within a definite interval of time.

$v=\frac{∆x}{∆t}$

Here, v is the average velocity $∆x$is the displacement in the time interval $∆t$.

Step 2: Calculation

$$\begin{gathered} \mathrm{Let} x_{1 }\mathrm{be} \mathrm{the} \mathrm{position} \mathrm{of} \mathrm{dodge} \mathrm{viper} \mathrm{at} \mathrm{the} \mathrm{time} t_1 \\ \mathrm{Let} x_2 \mathrm{be} \mathrm{the} \mathrm{position} \mathrm{of} \mathrm{dodge} \mathrm{viper} \mathrm{at} \mathrm{the} \mathrm{time} t_2 \\ \mathrm{Let} x_{3 }\mathrm{be} \mathrm{the} \mathrm{position} \mathrm{of} \mathrm{BMW} \mathrm{at} \mathrm{the} \mathrm{time} t_1 \\ \mathrm{Let} x_{1 }\mathrm{be} \mathrm{the} \mathrm{position} \mathrm{of} \mathrm{BMW} \mathrm{viper} \mathrm{at} \mathrm{the} \mathrm{time} t_2 \\ So, \\ {v}_1∆t=x_2-x_1 \\ {v}_2∆t=x_1-x_2 \\ \mathrm{Therefore}, \mathrm{we} \mathrm{can} \mathrm{write}, \\ {\mathrm{v}}_1∆\mathrm{t}=-({\mathrm{x}}_2-{\mathrm{x}}_1) \\ {\mathrm{v}}_2∆\mathrm{t}={\mathrm{v}}_2∆\mathrm{t} \\ \mathrm{Thus}, \mathrm{the} \mathrm{average} \mathrm{velocities} \mathrm{of} \mathrm{two} \mathrm{cars} \mathrm{are} \mathrm{equal} \mathrm{and} \mathrm{opposite}., \mathrm{i}.\mathrm{e},{\mathrm{v}}_1=-{\mathrm{v}}_2. \end{gathered}$$