Determine the velocity and displacement of the body after 5 seconds.
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1. Determine the velocity and displacement of the body after 5 seconds. The motion of the body is defined by the relation a = 4t2 where a in m/s2 and t in seconds. And it is known that S = 1 m and V = 1 m/s when t = 0.
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- 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.Equation of Motion(NORMAL AND TANGENTIAL) Fn= Man Ft= Mat Given a 1400 kg car that travels along a road with increasing vertical profile y = 0.0003x². If the constant velocity of the car is 30 m/s. of the distance is at 210m, a. Determine the x-component of the velocity (m/s) of the car. b. Compute the total force (KN). a. Determine the x-component of the velocity (m/s) of the car. b. Compute the total force (KN). Hint: The slope of a line is equivalent to tanø where Ø is an angle measured from the x-axis.The horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. The velocity of the plunger is v0 = 3.1 m/s in the position A where x = 0 and t = 0, and the deceleration is proportional to v so that a = -kv where k = 0.32 s-1. Find (a) the velocity when t = 2.9 s, (b) the position x when t = 2.9 s, (c) the velocity when x = 4.2 m.
- In the feasibility test, the flight movement of a drone is known to have a position function height h (t) = t2 - t - 2, where t is in minutes and height h is in meters. Determine the average speed of the drone increments at intervals of 3 minutes to 6 minutes and then determine the instantaneous velocity exactly equal to the average velocity.A particle moving along the s-axis has a velocity given by v = 22.3 -3.7t² ft/sec, where t is in seconds. When t = 0, the position of the particle is given by so = 3.9 ft. For the first 3.5 seconds of motion, determine the total distance D traveled, the net displacement As, and the value of s at the end of the interval. Answers: Total distance traveled, Net Displacement, The value of s at the end of the interval, D= As = S= i i i ft ft ftNeglect the diameters of the small pulleys and establish the relationship between the velocity of A and the velocity of B for a given value of y. If b = 1.00 m, y = 0.68 m, and VA = 2.98 m/s downward, what is the velocity of B (positive if downward, negative if upward). B Answer: VB = i m/s
- 2 The motion of a particle is defined by the relation. x=t²-10t+30 where, X in meters, t in sec. Determine 1 when the velocity is zero. (5 sec) 2 the position and total distance traveled when t≤ 8 sec (x+=8=14m, Distance = 39 m).An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular trackThe robot arm is elevating and extending simultaneously. At a given instant, 0 – 20°, – 24 deg/s - constant, I - 0.56 m, - 0.20 m/s, and i- 0.05 m/s?. Compute the magnitudes of the velocity v and acceleration a of the gripped part P. In addition, express v and a in terms of the unit vectors i and j. 0.69 m Answers: 0.56 m/s 0.24 m/s? V- ( i 0.01 i+ 0.55 j) m/s a - (i i + j) m/s? -0.101 0.0996
- t3 – 2t2 + 7 3. The motion of the particle along a straight line is governed by the relation a = where a is the acceleration in m/s² and t is the time in seconds. At time t = A second, the velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at timet = 2 seconds. - A = 1.476 second %3D 14.764 .m/s V = d = 218The 2-1b spool slides along the smooth horizontal spiral rod, r = (20) ft, where is in radians, as shown in (Figure 1). At the instant = 90°, its angular rate of rotation is constant and equals 0 = 4 rad/s. Figure 8 = 4 rad/s 1 of 1 P Determine the horizontal tangential force P needed to cause the motion. Express your answer in pounds to three significant figures. IVE ΑΣΦ ↓↑ vec P= 6.244 Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining ? lb2/38 The aerodynamic resistance to motion of a car is nearly proportional to the square of its velocity. Ad- ditional frictional resistance is constant, so that the acceleration of the car when coasting may be written = -C₁-C₂², where C₁ and C₂ are constants which depend on the mechanical configuration of the car. If the car has an initial velocity vo when the en- gine is disengaged, derive an expression for the dis- tance D required for the car to coast to a stop. a V.