9. A particle ofmass, m, moves along a straight line while subject to (1) a force proportional to its displacement x from a fixed point O in its path and directed toward O and (2) a resisting force proportional to its velocity. Write a DE for the motion of the particle.
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Formulate DE for problems involving newton's second law of motion (neat and clean solution)
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- a will be mass. a Travelled A particle of the where origin & by k constant. distance from Initially particle origin the and projected with speed "0" directly away from origin. Find the velocity of U= K particle function of "s". If what the minimum N distance the particle. is is m positive al the by attracted towards F= mk y² force of magnitude a 11 20³A particle of mass 1.5kg moves according to the equation x(t)=10t2, where x is in meters andtis in seconds. The force (in N) acts on the particle is Select one: a. 40 b. 35 с. 25 d. 30During a car collision, the knee, thighbone, and hip can sustain a force no greater than 4000 NN. Forces that exceed this amount could cause dislocations or fractures. Assume that in a collision a knee stops when it hits the car's dashboard. Also assume that the mass of the body parts stopped by the knee is about 20% of the total body mass. The person with a mass of 90 kgkg is initially traveling at 18 m/sm/s (40 mi/hmi/h). What minimum stopping time interval in needed to avoid injury to the knee? What is the minimum stopping distance?
- A particle of mass 2.5kg moves according to the equation x(t)-10t, where x is in meters and t is in seconds. The force (in N) acts on the particle is Select one: a. 25 b. 40 с. 35 d. 50A 2 kg mass initially moving with a velocity vi = 3x + 2y m/s is acted upon by a force F = 4x - 10y N for 5 seconds. What is the velocity of the mass at the end of that time? (the anser in vector forn)An arrow of mass 0.0025 kg is shot from a bow. If the string is stretched a distance m using a force 18 N, what would the resuling velocity be for the arrow when the string returns to its original position ?
- A mass (m) moves along the x-axis in the positive direction with a constant speed vo. At t=0, the mass passes through the origin and is subject to the force F = -Fo(x/H)e^(-x/H) for x >0. Fo and H are both positive constants. %3D a. Calculate the minimum initial speed required for the mass to pass through the origin and never turn back in terms of the constants m, Fo, and H. b. Write the velocity of m in unit vector notation, long after it crosses the origin (t>>0) and in the the case of vo>v0min where vomin is the result in part a.A 160 N net force acts right on a 20 kg object. If the initial velocity of the object is 20 m/s right, then what is the final velocity of the object after the net force has acted through a displacement of 50 m right?Problem 14: A particle of mass 1.39 kg begins at rest and is then subject to a force in the positive x direction that changes with time as given by the following function: F = mg[1-e33], where g is the acceleration due to gravity. 123 Av= Part (a) Determine the change in the velocity Av of the particle between tw0 and 13 seconds. m/s Part (b) Determine the change in x-coordinate of the particle Ar between r=0 and 1=1.3 seconds. G
- An object with a mass of 1.76 kg is initially at rest upon a horizontal, frictionless surface. An applied force of 3.04 N i acts on the object for 2.08 s. What is the object's final speed? Enter a number rounded to 2 decimal places and assume the answer has proper SI Units.A constant horizontal force of 37 N pushes a 20 kg mass through a medium that resists its motion with .9 N for every meter per second of speed. The initial velocity of the mass is 7 meters per second in the direction opposite of the applied force. Find the velocity of the mass after 25 seconds.As shown in the graphs below, the variable and its components are subjected to forces with Px and Py. A particle of remaining 4 kg mass has initial velocity components vx, 0 = 10m / s and vy, 0 = 5m / s. a) What are the velocity components of the particle after 2.5 s? b) What are the velocity components of the particle after 5 s?