What Time Achieves Maximum Velocity on a Rollercoaster?

[Phoenon]

Homework Statement

The velocity of a a rollercoaster can be described by the fomula "v(t) = -sint + 2sin2t". The interval is 0-5. At what time and what magnitude is maximum velocity achieved?

Homework Equations

v(t) = -sint + 2sin2t

The Attempt at a Solution

v(t) = -sint + 2sin2t
v'(t) = 4cos2t - cost
4cos2t = cost
(not allowed to use graphing calculator)
Answer should be 4.

 

[hunt_mat]

Write:

$$\cos 2t=\cos^{2}t-\sin^{2}t$$

now use $$\sin^{2}t+cos^{2}t\equiv 1$$ to turn sin into cos and you will be left with a quadratic equation in cos t, solve it.

 

[tiny-tim]

Welcome to PF!

Hi Phoenon! Welcome to PF!

The velocity of a a rollercoaster can be described by the fomula "v(t) = -sint + 2sin2t". The interval is 0-5. At what time and what magnitude is maximum velocity achieved?
…
Answer should be 4.

Are you sure that's the right question?

2sin2t - sint can't possibly be as much as 4.

 

[hunt_mat]

Hi Phoenon! Welcome to PF! Are you sure that's the right question?

2sin2t - sint can't possibly be as much as 4.

scrap that, I made a mistake