The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial velocity of the object is v(0) = - 9 m/s. Use antiderivatives to find an equation v(t), the object's velocity v(t) =

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

A rocket sled having an initial speed of 112 mi/h is slowed by a channel of water. Assume that during the braking process, the acceleration a is given by a(v) = −µv², where v is the velocity and is a constant. Find the time ☛ required to slow the sled to 10 mi/h as a function of u. T hours

An object of mass 5 kg is released from rest 3000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec and let x(t) represent the distance the object has fallen in t seconds. dv First write mat = mg - bv, v(0)=v in terms of the given information. v(0) =