4. A body experiences acceleration "a" given by the expression a = At - Bt?, where A and B are constant and t is time. If, at time t=0, the body has zero displacement and velocity, at what next value of time does the body again have zero displacement?
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- When a particle travels in a uniform circular motion, all the following stay constant excluding: A)Radius B)Acceleration C)Speed D)VelocityThe elevator in an office building, starting from rest at the first floor, is accelerated 0.75 m/sec2 for 5 secs. It continues at constant velocity for 12 secs, more and is then stopped in 3 secs with constant deceleration. If the floors are 3.75 m apart, at what floor did the elevator stop?A car moves along a straight line whose equation of motion is given by V =4t2-3t+1 where (V) is in meter per second and (t) is in seconds. After 3 seconds from the start the linear displacement was 27m. When t = 7 seconds, determine the linear displacement, linear velocity and linear acceleration of the car.
- Q) A driver is driving a car in a circular ring which is 120 m in diameter. At one instant, his total acceleration is 12 m/s2 with a direction of 30° relative to the tangent. a) Determine his radial and tangential acceleration. b) Starting from the state described above and maintaining the same tangential acceleration, how long does he need to perform one complete circuit?2.A train moving with a constant acceleration travels 7 m/sduring the 10th sec of its motion and 5 m/s during the 12thsec of its motion. Find its initial velocity and its constantacceleration.A nozzle is designed to move a liquid from V1 velocity to V2 in a linear fashion. The linear relationship here is V = ax + b and a and b are constant. As the flow is constant with V1 = 10 m / s at x1 = 0 and V2 = 25 m / s at x2 = 1m; a) local (local) acceleration, b) Convective acceleration (convective acceleration), c) Determine the acceleration of the liquid at the points x1 = 0 and x2 = 1 m.
- This most likely is made to be a probelm about mx''+bx'+kx=f(t) m = mass b = friction k = spring constant 4. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is atequilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a mediumwhere friction is small, and we assume it is zero. Note that the acceleration due to gravity near theearth’s surface where the experiment takes place can be taken as 32 ft/s2.(a) Suppose that in addition to the conditions described above, a hammer strikes the mass everyπ/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models theforce of each blow to the mass. Find the function x(t) for the displacement from equilibrium infeet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use ofunit step or Heaviside functions and such that in each time window it is a different multiple of the samesinusoidal function.(b) Now assume the same spring-mass…2.A train moving with a constant acceleration travels 7 m/sduring the 10th sec of its motion and 5 m/s during the 12th sec of its motion. Find its initial velocity and its constantacceleration. (show your complete solution)A boat is towed at the rate of 12mi/hr. At t = 0, the towing line is cast off and a man in the boat begins to row in the direction of motion exerting force of 20 lb. The combined weight of the man and the boat is 480lb. The water resists the motion with a force equal to 1.7v lb, where v is the velocity of the boat in feet per second. Derive a DE leading the velocity of the boat.
- line rotates in a vertical plane according to the law θ = t^3-2t^2 - 2 , where θ gives the angular position of the line in radians, (t) is the time in seconds, The line is turning clockwise when t=1 sec, Determine A- The angular acceleration when t = 3 sec. B- The value of(t) when the angular velocity is zero C-the total angle turned through during the time t=1 sec to t=3 sec.At time zero, a particle is at x = 4.0 m and y = 3.0 m and its velocity v is given in diagram H. The particle has a uniform acceleration a of given by the equation in diagram H. What is the object’s position at time t = 4.0 s? SEE ATTACHED DIAGAM WHICH ONE IS CORRECT? A. None of the other answers B. (20, -21) m C. (33, 18) m D. (44, -9.0) mA shaft rotating with 10 rev/s is uniformly accelerated at 0.3 rad/s2 for 8 seconds. It then rotates with a uniform speed for next 10 s. Then it is made to stop in next 20 s. Determine (i)maximum angular velocity; (ii) total angular displacement The maximum velocty in rad/s is The total displacement in rad is