In figure below, the area under the velocity-versus-time graph and between the vertical axis and timet (vertical dashed line) represents the displacement. As shown, this area consists of a rectangle and a triangle. Slope = a (a) Compute their areas. (Use any variable or symbol stated above as necessary.) Arectangle Atriangle (b) Explain how the sum of the two areas compares with the expression on the righthand side of x, = x + vt +a t..
In figure below, the area under the velocity-versus-time graph and between the vertical axis and timet (vertical dashed line) represents the displacement. As shown, this area consists of a rectangle and a triangle. Slope = a (a) Compute their areas. (Use any variable or symbol stated above as necessary.) Arectangle Atriangle (b) Explain how the sum of the two areas compares with the expression on the righthand side of x, = x + vt +a t..
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Velocity versus Time Graph and Displacement Calculation**
In the figure below, the area under the velocity-versus-time graph and between the vertical axis and time \( t \) (vertical dashed line) represents the displacement. This area consists of a rectangle and a triangle.
**Graph Explanation:**
- The graph is marked with the velocity axis \( v_x \) and time axis \( t \).
- Initial velocity is \( v_{xi} \) and final velocity is \( v_{xf} \).
- The time interval is denoted by \( t \).
- The slope of the line is \( a_x \), representing acceleration.
- The rectangle has height \( v_{xi} \) and width \( t \).
- The triangle has a height difference \( v_{xf} - v_{xi} \) and the same base width \( t \).
**Tasks:**
(a) **Compute their areas.** (Use any variable or symbol stated above as necessary.)
\[
A_{\text{rectangle}} =
\]
\[
A_{\text{triangle}} =
\]
(b) **Explain how the sum of the two areas compares with the expression on the right-hand side of \( x_f = x_i + v_{xi}t + \frac{1}{2}a_x t^2 \).**
[Provide your explanation here.]
---
This exercise involves calculating the area under a graph to find displacement and understanding how it relates to the kinematic equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c9518c-3072-47cd-a223-037446775cff%2Fd6b61c06-93a7-4197-8562-d163344543b5%2Fr1vfsl6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Velocity versus Time Graph and Displacement Calculation**
In the figure below, the area under the velocity-versus-time graph and between the vertical axis and time \( t \) (vertical dashed line) represents the displacement. This area consists of a rectangle and a triangle.
**Graph Explanation:**
- The graph is marked with the velocity axis \( v_x \) and time axis \( t \).
- Initial velocity is \( v_{xi} \) and final velocity is \( v_{xf} \).
- The time interval is denoted by \( t \).
- The slope of the line is \( a_x \), representing acceleration.
- The rectangle has height \( v_{xi} \) and width \( t \).
- The triangle has a height difference \( v_{xf} - v_{xi} \) and the same base width \( t \).
**Tasks:**
(a) **Compute their areas.** (Use any variable or symbol stated above as necessary.)
\[
A_{\text{rectangle}} =
\]
\[
A_{\text{triangle}} =
\]
(b) **Explain how the sum of the two areas compares with the expression on the right-hand side of \( x_f = x_i + v_{xi}t + \frac{1}{2}a_x t^2 \).**
[Provide your explanation here.]
---
This exercise involves calculating the area under a graph to find displacement and understanding how it relates to the kinematic equation.
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