Consider an object moving along a parametric curve whose position vector at time tis given byr(t)=e2tcos(2t)i+e2tsin(2t)j+3e2tk(a) Compute the velocity v(t) and the acceleration a(t)of the object.(b) Compute the object's speed v(t) and the exact arclength sof the part of the curve between t=0 and t=2.(c) Find the unit tangent vector T(t).(d) Calculate the curvature .(e) What happens to the curvature ast? Looking at the equation for r(t),explain why the curvature changes in this way ast increases.