\(m=\dfrac{y_2-y_1}{x_2-x_1} \) use this formula
\(\dfrac{1}{√3}\)
\(\dfrac{-1}{√3}\)
\({√3}\)
\(-{√3}\)
Since the particle gets reflected upon hitting the x-axis, the angle of incidence is equal to the angle of reflection.
(In other words, the angle the particle makes with the x-axis before hitting the x-axis is the same as the angle it makes with the x-axis after reflection.)
The initial position of the particle is \((0, 1)\) and the point where it gets reflected is \((√3, 0)\). The slope of the line connecting these two points is given by:
\(m=\dfrac{0-1}{√3-0} =\dfrac{-1}{√3}\)
Hence Slope of the line is \(\dfrac{-1}{√3}\)
Given:
Initial Position: The particle starts at (0, 1).
Reflection Point: Upon hitting the x-axis, the particle reflects at \((\sqrt{3}, 0)\).
Calculate Slope:
The slope m between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Substitute the coordinates:
\(m = \frac{0 - 1}{\sqrt{3} - 0}\)
Perform Calculation:
Numerically compute the slope: \(m = \frac{-1}{\sqrt{3}}\)
Interpret the Result:
The negative sign indicates that the line slopes downward from left to right.
\(\frac{1}{\sqrt{3}}\) simplifies to \(\frac{\sqrt{3}}{3}\).
The slope of the line connecting the initial position (0, 1) to the reflection point \((\sqrt{3}, 0)\) is \(\frac{-1}{\sqrt{3}}\).
So, the correct option is (B): \(\frac{-1}{\sqrt{3}}\)
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
A slope of a line is the conversion in y coordinate w.r.t. the conversion in x coordinate.
The net change in the y-coordinate is demonstrated by Δy and the net change in the x-coordinate is demonstrated by Δx.
Hence, the change in y-coordinate w.r.t. the change in x-coordinate is given by,
\(m = \frac{\text{change in y}}{\text{change in x}} = \frac{Δy}{Δx}\)
Where, “m” is the slope of a line.
The slope of the line can also be shown by
\(tan θ = \frac{Δy}{Δx}\)
Read More: Slope Formula
The equation for the slope of a line and the points are known to be a point-slope form of the equation of a straight line is given by:
\(y-y_1=m(x-x_1)\)
As long as the slope-intercept form the equation of the line is given by:
\(y = mx + b\)
Where, b is the y-intercept.