The acceleration of a particle is defined by the relation a=-kx² where a in m/s², X in meters. the particle starts with no initial velocity at x = 12 m, and its velocity is 8 m/sec when X=6m. Determine the value of k 11 the value of k. [324 m²³/s²] 16 the velocity of the particle when X=3m [13.26m]
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- 2.68 0. CALC An object's velocity is measured to be v,(1) = a – Bt², . 4.00 m/s and B = 2.00 m/s. At t = 0 the object is at x = 0. (a) Calculate the object's position and acceleration as functions of time. (b) What is the object's maximum positive displacement from the origin? where a =An object is dropped from rest and takes 2.25 seconds to reach the ground below. From what distance above the ground was it dropped? State this as a positive number and assume it has proper SI Units.The velocity of a rocket is given as a function of time by v(t) = A(1 – e-bt) for 0 , t , 30 s, where the constants A = 150 and b = -0.15. [ d/dx (e-ax dx) = -a e-ax; ∫ e-ax dx = -1/a e-ax ] a) What are the SI units of A and b? b) What is the speed of the rocket at t = 10 s? c)Find the displacement of the rocket in the first 10 s ( from t = 0 s to t = 10 s)
- The velocity of a particle moving along the x-axis is defined by V= kx3 – 4x2 +6x, where V is in m/sec., x is in meters, and k is a constant. If K=1 Compute the value of the acceleration after x= 2 meters.The acceleration of an object (in m/s2) is given by the function a(t)=7sin(t)a(t)=7sin(t). The initial velocity of the object is v(0)=−1v(0)=-1 m/s. Round your answers to four decimal places. v(t) = -7cos(t) + 6 The objects displacement from time 0 to 3 is: 17.01216 meters Find the total distance traveled by the object from time 0 to time 3.The acceleration of an object (in m/s2) is given by the function a(t)=8sin(t)a(t)=8sin(t). The initial velocity of the object is v(0)=−10v(0)=-10 m/s. Round your answers to four decimal places.a) Find an equation v(t) for the object velocity.v(t)v(t) = −8cos(t)−2Correct b) Find the object's displacement (in meters) from time 0 to time 3.3.4187Incorrect metersc) Find the total distance traveled by the object from time 0 to time 3. meters
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