Question

the vector function r(t)=< 5 sin t, 3 sec t > , represents the position of a particle at time t. find the velocity v (t) and acceleration a (t).

I don't know how to solve it without the t given. Please help

Answer 1

v(t) = dr/dt = <5cost, 3sect tant>
a(t) = dv/dt = <-5sint, 3sect(2sec^2t-1)>

just do normal derivatives of trig functions

Answer 2

Find the area of the shape shown below.





units2\text{units}^2units
​2
​​u, n, i, t, s, start superscript, 2, end superscript