A particle is moving with the given data a(t)= 3e^2t -2 cost, s(0)=0 and v(0)=0, find the position of the particle.

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

An automobile, traveling at a constant rate, starts at home at time t = 0 and ends up 10 hours later 200 miles from home. It than changes speed and continues for the next 10 hours ending up 300 miles from home. It takes another 10 hours for it to return home. On two separate set of axes, sketch graphs of the distance and velocity functions.

The surface area S of a metal cylinder is given by S = 2ar² + 2rh where r is the radius and h is the height. The height can be cut to a relative accuracy of 3% but the radius can only be cut to a relative accuracy of 5%. if the cylinder is supposed to have a radius of 6 cm and a height of 10 cm, use differentials to eștimate how bad the relative accuracy of the surface area can be. Don't round anawes unless the instructions request approximations, or as part of checking your Own work.