Derivatives of Trig Functions: Applications
3. The displacement of a particle is given by s = 2t sec t1/2. Determine the velocity of the particle when t = 0.04.
Velocity is the derivative of displacement with respect to time:
v = ds/dt = 2 sec t1/2 + 2t [1/2 t-1/2 sec t1/2 tan t1/2]
(Note that we used the Product Rule there.)
v = 2 sec (0.04)1/2 + 2(0.04) [1/2 (0.04)-1/2 sec (0.04)1/2 tan (0.04)1/2] = 2.082
