**Title: Matching Kinematic Equations with Their Integrated Forms****Question 16:** Match the following basic kinematic equations to their respective integrated form at constant acceleration:1. **\( v = v_0 + a_c t \)** 2. **\( v^2 = v_0^2 + 2a_c (s - s_0) \)** 3. **\( s = s_0 + v_0 t + \frac{1}{2} a_c t^2 \)** **Integrated Forms:**1. **\( v = \frac{ds}{dt} \)** 2. **\( a = \frac{dv}{dt} \)** 3. **\( a\, ds = v\, dv \)** ### Explanation of Diagrams:- **Equation 1:** Represents the relationship between velocity (\(v\)), initial velocity (\(v_0\)), acceleration (\(a_c\)), and time (\(t\)). It's a linear relation describing how velocity changes over time.- **Equation 2:** Relates the square of velocity to initial velocity squared, acceleration, and the change in position (\(s\)). It is derived from the work-energy principle and links kinetic energy with distance.- **Equation 3:** Describes position (\(s\)) over time with constant acceleration. It integrates initial position, initial velocity, and acceleration, providing a quadratic relationship between position and time. **Q24.** The buoyancy force on the 580-kg balloon is \( F = 6 \, \text{kN} \), and the air force acting on the balloon is \( \mathbf{F}_{\text{air}} = \left\{ C_1 \cdot t \, \mathbf{i} - C_2 \cdot \sqrt{t} \, \mathbf{j} \right\} \, \text{N} \), when \( t \) is time in seconds, constants \( C_1 = 24 \) and \( C_2 = 240 \). If the balloon starts from rest, determine its speed after 28 seconds. Neglect the size of the balloon but don’t neglect its weight. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper SI unit. Take \( g = 9.81 \, \text{m/s}^2 \).**Diagram Explanation:**The diagram shows a hot air balloon with colored stripes. It includes the following labels:- An upward arrow labeled \( F = 6 \, \text{kN} \) indicating the buoyancy force.- A leftward arrow labeled \( \mathbf{F}_{\text{air}} \) indicating the air force.- Coordinate axes labeled \( x \) and \( y \).**Your Answer:**Answer: [Your calculation here] units

Q16. Match the following basic kinematic equations to their respective integrated form at constant acceleration: < < v = vo + act 1. v = s = so + vot + act² S v² = v² + 2ac (s − so) 2. a = dv dt ds dt 3. ads - vdv

Q16. Match the following basic kinematic equations to their respective integrated form at constant acceleration: < < v = vo + act 1. v = s = so + vot + act² S v² = v² + 2ac (s − so) 2. a = dv dt ds dt 3. ads - vdv

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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