A particle's position (in meters) is given by the equation s(t) = 5x sin(2x), on the interval [-1, 4] minutes. What is its instantaneous velocity at t=0

Answer 1

Taking the derivative of the function, we get 5sin(2t) + 10tcos(2t). If you plug in t=0, you get an instantaneous velocity of 0 m/s (because sin0 = 0 and the second term has 10(0) = 0).