**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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The location of the tool, VT, is not accurately known. Using force control, the robot feels around with the tool tip until it inserts it into the socket (or Goal) at location ST. Once in this "calibration" configuration (in which {G}and {T) are coincident), the position of the robot, T, is derived by reading the joint angle sensors and computing the kinematics. Assuming T and Tare known, give the transform equation to compute the unknown tool frame, WT. {B} {S} {W} 2G {G} ÎT {T} ☆G XT 2T
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The following EOMS describe the behavior of an electric motor attached to a torsional spring and damper: [Li + Rz + vb = Vin(t) IÖ= k0b0 + T Importantly, the equations are coupled by the fact that 7 = k₁z and v₂ = k₂0. Here, L, R, kv, I, k, b, and kt are constants. z is the current in the motor, and is the angular displacement of the motor (clearly then, is the motor's angular velocity). Finally, the input to the system is vin (t). Your tasks: A Substituting in the coupling terms (7 = ktz and v k0) into the EOMs, write the state space form of the system x = Ax + Bu, assuming your states are x₁ = z, x₂ = 0, and x3 = 0. Clearly identify your matrices. B Assume that the desired outputs of the system (to be measured) are the current z, the angle and the input Vin all as separate elements in the vector y. Write the output equation y = Cx + Du. Hint: D will NOT be zero in this case. Clearly identify your matrices C Assume there is no stiffness to the spring (k = 0). Using w(t) to represent…
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TUNE FLE SPAN FM AutoSave Hwk-6a.MechanialProperties-ElasticRegion • Last Modified: Mon at 9:05 AM - On O Search (Alt+Q) Torialai Stanikzai TS File Home Insert Draw Design Layout References Mailings Review View Help P Co - A^ A Aav AoEE E- E E T O Find Times New Roma v 12 AaBbCcDc AaBbCcDc AaBbC AABBCCC AaB AABBCCC AaBbCcDa AaBbCcDa AaBbCcDa Paste BIU ab x, x Ave Av 目三==。、田、 S Replace S Format Painter 1 Normal 1 No Spac. Heading 1 Heading 2 Title Editor Subtitle Subtle Em. Emphasis Intense E.. Dictate A Select v Clipboard Font Paragraph Styles Editing Voice Editom A tensile stress is applied axially on a cylindrical brass rod with diameter of 10mm. Determine the magnitude of the load required to produce a 2.5 x 10-3mm change in diameter if the deformation is entirely elastic. The Young's modulus for brass 3. is 97 GPa and the Poisson value is 0.34.
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