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The positions, of a particle moving along a horizontal straight line is given by the equation s =


6t² - 4, where s is in meter and t is the time in seconds. The particle is 4m to the right of the


origin when t = 0.


A.1. Determine the displacement of the particle during the time interval from t = 2s to t = 4s.


A.2. Determine the velocity and acceleration of the particle when t = 4s.

A vehicle with a mass of 1 200 kg accelerates uniformly, from rest up a gradient of 1 in 25 and reaches a speed of 54 km/h after 2 minutes.Calculate The kinetic energy that the vehicle possesses at the end of the 2 minutes


In fig . The pressure at point a is 172 kpa





What is the name given to the type of diagram shown in Fig. 4(a)? (1 mark) (ii) Using Fig. 4(a), give a clear account of the development, during slow cooling, of the microstructure in an iron – carbon alloy with a carbon content of 0.25 wt% C. Your answer must give an account at each of the points A, B, C, and D shown on Fig. 4(a). (7 marks) (iii) What specific name is given to the iron – carbon alloy with a composition of less than 0.76 wt% C? (2 marks) (iv) Identify how the material structure changes as the wt % C increases from 0 to 1.2% and draw a sketch to show how the tensile strength, ductility and hardness of the material are affected as a result.


A small metal bar, whose initial temperature was 20° C, is dropped into a large container of boiling water. How long will it take the bar to reach 90° C if it is known that its temperature increases 2° in 1 second?


How the number of ripples is related to the number of harmonics in the



synthesis of the periodic train of square

1)Find the spectral components of a periodic train of a square pulse with an even symmetry by applying Fourier series analysis. Consider the period of 1 s for the repetition of the square pulse.


2) Why do you observe ripples in the synthesis of the periodic train of square pulse?




(4) Why are the ripple absent in the synthesis of the periodic train of triangle pulse?


5)How the number of ripples is related to the number of harmonics in the synthesis of the periodic train of square pulse?





(6) What is the effect of varying the number of samples and the frequency as in the steps (7) and (8), respectively?

a mixture containing 800 kg of naoh,300 kg of al2o3 and 600kg of hf is heated to 950 °c and reacts to completion. what is the maximum masss of na3alf6 is formed ?

The hoist in a mine shaft has a mass of 5 tons. The vertical distance of the mine shaft is 500 m. the hoist is moving at a constant velocity upwards in the mine shaft. a. Determine the work done of the hoist. b. If it takes the hoist 5 minutes to reach the surface, then calculate the power.


1. a particle moves with a simple harmonic motion in a straight line. at t=0, the acceleration is 3 m/s²,the velocity is 1m/s and the displacement is "-0.30m." find the amplitude and the period of motion



2. brine from a first tank runs into a second tank at 2 gal/min, and the brine from the second tank runs into the first at 1 gal/min. initially, there are 10 gallons of brine containing 20 lb of salt in the first and 10 gallons of fresh water in the second tank. how much salt will there be in the first tank after 5 min?

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