Two particles P and Q start from rest at the origin s=0 and move along a straight line with acceleration given by ap = 8t-2 and aq = 12t2-8, where acceleration is in m/s2 and t is in seconds. Determine the distance between the
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- The motion of a particle is defined by the function x = at3 - bt2 - ct + d where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft high. How high from the top of the building will the ball go? Consider two objects moving along x-axis are starting at the same time. Their positions are measured in centimeters at time t in seconds. If the equation of motion of objects 1 and 2 are s1 = 2t2 -3t and s2 = 3t-t2 respectively, determine the distance between the objects at the instant when they have the same velocity. If , x = Arctant3 , y = √1+t6 find the value of a if 2ay'' / y' when t =√2A car moves along a straight line whose equation of motion is given by V =4t2-2t+2 where (V) is in meter per second and (t) is in seconds. After 3 seconds from the start the linear displacement was 35m. When t = 6 seconds, determine the linear displacement, linear velocity and linear acceleration of the car.
- The motion of a particle is defined by the parametric equations ax =0.8t, ay =2–0.3t, az =5 where “a” is in m/s2 and t in seconds.The particle is at rest and is placed at the origin at t = 0. What is the acceleration of the particle after 10 seconds? What is the velocity of the particle after 10 seconds?The position x of a particle varies with time as x = at² - bt³. The acceleration of particle is zero at time I equal to a A B D JIE b 2a 3b a 3b Zero• 1. A particle position given by s(t) = 4 t2 - 32 t +36 with s in meters and t in seconds. At what position does the particle come to a # 1 %3D momentary stop to reverse its motion? par • 2. A particle moves in a straight line such that for a short time its velocity is defined by V = ( 4t3 + 3t2 seconds. Determine its position and acceleration when t = 3 s; 2t) ft/s, where t is in %3D %3D he when t = 0, S = 0 %3D e pa he particle for wertical disola reach the ground tance that the paticle travel haght of the paratle, he t lury paricle when the bonzonl distence i 70 m dislmce whn the hayht uf the paricle is %23
- F(t) K: 3. A particle with a mass of 3 kg has velocity = 5î + 7ĵ- 3km/s. The total force acting on the particle is given by F = 3Aî - 2Aĵ + 4Ak N, where A is an unknown constant. Determine the value of A such that the x-component of the particle's velocity is 10 m/s after the force is applied for 2 seconds. Also determine the particle's velocity vector at this time.The position of a particle as a function of time t, is given by x(t) = at +bt² - ct³ where a, b and care constants. When the particle attains zero acceleration, then its velocity will be? A B с D a+ E + a+ a+ b² 4c b² 2c b² 3c2-3.31 A sport car starts from rest in a road closed to traffic such that its V speed is described by the v-s graph shown in Fig. 2-3.31. (For s=0; v₁ v₁ = a₁ = 0) In this graph; s = 120m, Sg=360m, v₁ = 40m/s and V = 10 m/s. Determine the accelerations of the sport car when it passes from s=72m and s= 200m. Draw the a-s graph. VB Fig. 2-3.31 SB S
- The y-coordinate of a particle in curvilinear motion is given by y = 9.6t3 - 7.7t, where y is in inches and t is in seconds. Also, the particle has an acceleration in the x-direction given by ax = 2.3t in./sec2. If the velocity of the particle in the x-direction is 4.5 in./sec when t = 0, calculate the magnitudes of the velocity v and acceleration a of the particle when t = 2.0 sec. Construct v and a in your solution.Answers: When t = 2.0 sec,A body moves along a linear path and its rate of change of velocity varies with time and is written as a=2-3t, where t is the time in second. After 5 second, from start of observation its velocity is determined to be 20 m/s. After 10 second from start of observation, the body is at 85 m far from the origin. Determine the following:a. Rate of change of velocity and velocity at the start of motion.b. Distance from the origin at the start of observationc. Time after start of observation in which the velocity becomes zero.3. The motion of the particle along a straight line is governed by the relation a = t³ – 2t2 + 7 where a is the acceleration in m/s? andt is the time in seconds. At time t velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at time t = 2 seconds. * A second, the 0.5 А second V = ..m/s d 25 m