A particle's velocity is given by the function Vx = (2.2 m/s) * sin (pi * t), where t is in seconds. What is the first time after t=0 s when the particle reaches a turning point?

After 1 seconds

Explanation:

The velocity of the particle is given by a periodic function, in the form

[m/s]

where

t is the time, in seconds

A periodic function is written in the form

where

A is the amplitude (maximum displacement from equilibrium position)

is the angular frequency, which can be written as

where T is the period.

For the periodic function in this problem, we have

A = 2.2 m/s

[rad/s]

So the period is:

The particle reaches a turning point when the velocity becomes zero, and then it becomes negative.

At t = 0, the function has value of zero.

After 1/4 of period, which corresponds to 0.5 seconds, the function reaches its maximum:

After 1/2 of period, which corresponds to 1 second, the function becomes zero again:

Therefore, the particle reaches the first turning point at t = 1 sec.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.