The displacement of an oscillating mass is given by x(t) = 20 cos( 5 t ). at time t = 0.5π s, what is the acceleration of the mass in m/s2?

The speed of the object is the 1st derivative of its displacement.

The acceleration is the 2nd derivative of the displacement.  That's also the first derivative of speed.  Either way you approach it, we have to take the displacement and differentiate twice.

Displacement = x(t) = 20 cos(5t) meters

Speed = x'(t) = -100 sin(5t) m/s

Acceleration = x''(t) = -500 cos(5t)  m/s²

At time  t=0.5π sec,

Acceleration = -500 cos(2.5π)  m/s²

cos (2.5π) = cos(0.5π) = zero

This is weird.  At  t=0.5π sec, the acceleration of the oscillating mass appears to be zero.

My math must be kerflooie, but I'm too tired right now to stay and pick at it.  I'll just resign myself to having my answer reported, and I hope whoever reports it will be kind enough to point out the error of my ways.

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50

option number c is the right answer.