A particle in an experimental apparatus has a velocity given by v = k vs, where v is in millimeters per second, the position s is millimeters, and the constant k = 0.2 mm 's. If the particle has a velocity vo = 3 mm /s at t = 0, determine the particle position, velocity, and acceleration as functions of time, and compute the time, position, and acceleration of the particle when the velocity reaches 15 mm /s.

Question 4 The macroscopic model developed by Drake et al. (1967) proposed the following equation to express the relationship between speed and density: ● v = vfe A traffic engineer calibrated the model using empirical data and the model parameters were estimated as follows: The free-flow speed (vf) = 110 km/h The density at capacity (km) = 30 veh/km Answer the following questions: 2 (二)ㄕ a) Develop an equation to express the flow (q) as a function of the speed (v). b) Using the equation developed in the previous question, plot the q-v relationship, with (v) on the horizontal axis and (q) on the vertical axis. (Show all critical values on your plots). c) Calculate the average headway and the average spacing corresponding to the capacity.

An Atwood's machine was used by a student to determine the acceleration of two masses, m₁=73 grams and m2=70 grams. The pulley rotates freely, and the masses were released from rest and the vertical distance traveled by the masses is 80 cm. The student conducted 5 trials to measure the time it took the masses to travel the vertical distance of 80 cm. The measured time were 3.23 s, 3.08s, 3.43s, 3.29s and 3.67s. If the mass of the pulley is 95.74 grams determine: a. The experimental value of the acceleration b. The true value of the acceleration c. the percent difference between the experimental and true values of acceleration.

The discharge of oil from a tank through an orifice is to be modeled using water as the flowing fluid. The kinematic viscosity of the oil is eight times that of the water. The relative density of the oil is 0.90. What oil flowrate is represented by 0.002 2 m'/s in the model? If the force exerted on the model tank bottom is 210 N, what is the corresponding force in the prototype? 1.2 md Oil 12 m 0.2 m d

8. A particle is displaced from the equilibrium position by a distance 1=1.0 cm and then left alone. What is the distance that the particle covers till its oscillations die down, if the logarithmic decrement is equal to λ = 0.020? [Answer: s=2 m nearly]

If the particle starts from rest, what is its velocity, m/s, at t = 4 s? a (m/s) 10 t(S) 2 4

Example 2: The acceleration of a particle moving along a straight line is a = Vs m/s?, where s is in meters. If its position s = 0 and velocity v = 0 when t= 0, determine its velocity when s = 16 m. What time is that? ds V = dt dv ads = vdv dt