a particle moves in a straight line such that its position x from a fixed point 0 at time 't' is given by

Question

x= 5 + 8sin2t + 6cos2t

1. Find the period and amplitude of the particle.

2. Find the greatest speed of the particle.

Thanks

Answer 1

amplitude=10
period is also 2pi

dx/dt = 16cos2t - 12sin2t
amplitude = 20, so that would be its maximum speed.

Answer 2

Can you please explain how to get the answers please?