A model known as stopping sight distance is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by v2 + TV, 2g(f + G) where we have the following. S = stopping sight distance (ft) V = initial speed (ft/s) g = acceleration due to gravity, 32.2 ft/s2 f = coefficient of friction between tires and roadways
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- The speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.PA-4 (For Automobile Mechanics). One of the more well-known tests is crash testing. The car is timed and recorded going in two separate and opposite directions. The two times are averaged together to achieve the commonly accepted 0 to 60 time. Given this brief review, let us suppose that the velocity (in feet per second) of an automobile starting from rest is given by this model v = 80t/(t + 5). Determine the velocity and acceleration of the mobile when t=0, t=10, t=20, t=30, t=40, t=50, and t=60.1. Circle weather the following statements are true or false. If the statement is true justify your reasoning if the statement is false correct the statement to make it true or justify why it is false a. Impulse is the integral of a force vs distance graph b. In two dimensions analyzing linear and angular momentum provides up to three scalar equations. c. Linear acceleration and angular acceleration both have units of ft/s^2 or m/s^2 d. When absolute motion or a rigid body it is important to find a function that relates linear and angular position then integrate to find velocity e. Instantaneous centers can only be determined for velocity and only for a snapshot in time
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- You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)For the Following question Graph all 4 : [I just need all 4 graphs and please explain and make clean solution] Position vs time Velocity vs time Acceleration vs time Force vs time [For your convenience, I have solved the numerical solutions for the problem] (Please Look at the picture since it is much cleaner) Question : A 550 kilogram mass initially at rest acted upon by a force of F(t) = 50et Newtons. What are the acceleration, speed, and displacement of the mass at t = 4 second ? a =(50 e^t)/(550 ) [N/kg] v = ∫_0^t▒(50 e^t )dt/(550 )= v_0 +(50 e^t-50)/550=((e^t- 1))/11 x = ∫_0^t▒(e^t- 1)dt/(11 )= x_0 +(e^t- t - 1)/(11 ) a(4s)=(50*54.6)/550= 4.96[m/s^2 ] v(4s)=((e^4-1))/11= 4.87[m/s] x(4s)=((e^4- 4 - 1))/11= 4.51 [m]I have data accrued from a fan could you explain to me the concepts and show me how to calculate the horsepower and work done by the fan that data was composed of below in this table? Time (s) Run #1 Velocity, Blue (m/s) Run #1 0.05 0 0.1 0 0.15 0 0.2 0 0.25 0 0.3 0 0.35 4.04E-04 0.4 4.04E-04 0.45 0 0.5 -4.04E-04 0.55 -4.04E-04 0.6 0 0.65 0 0.7 4.04E-04 0.75 8.08E-04 0.8 4.04E-04 0.85 -4.04E-04 0.9 -8.08E-04 0.95 0 1 8.08E-04 1.05 4.04E-04 1.1 0 1.15 -4.04E-04 1.2 0 1.25 4.04E-04 1.3 0 1.35 0 1.4 -4.04E-04 1.45 0 1.5 4.04E-04 1.55 0 1.6 0 1.65 -4.04E-04 1.7 0 1.75 4.04E-04 1.8 0 1.85 0 1.9 -4.04E-04 1.95 0 2 4.04E-04 2.05 4.04E-04 2.1 4.04E-04 2.15 0 2.2 0 2.25 0 2.3 0 2.35 0 2.4 0 2.45 0 2.5 4.04E-04 2.55 8.08E-04 2.6 8.08E-04 2.65 8.08E-04 2.7 8.08E-04 2.75 8.08E-04 2.8 4.04E-04 2.85 0 2.9 0 2.95 0 3 0 3.05 0 3.1 0 3.15 0 3.2 0 3.25 0 3.3 0 3.35 0…