A particle moves along the x − axis so that its position, x(t) at the time t is given by x(t)=-1/2cos(-2t^3)

Question

a). Find the acceleration of the particle at t=2

b). Find the average acceleration of the particle on the time interval [1,3]

Answers should be up to the 3rd decimal place in accuracy, units are not required.

Answer 1

a). Find the acceleration of the particle at t=2

b). Find the average acceleration of the particle on the time interval [1,3]

Answers should be up to the 3rd decimal place in accuracy, units are not required.

X(t) = -1/2 Cos (-t³ )

Cos (-theta ) = Cos ( theta)

X(t) = - 1/2 Cos(t³)

dX/dt = = 3/2 * t² *Sin (t ³ ) = velocity = V

Acceleration = dV /dt = a

= 3/2* ⌈3 ⌉t ⁴ * Cos(t ³ ) +2t * (sin t³) ⌉

= 9/2 t⁴ * cos ( t ³ )+3t * Sin (t ³ )

Plug in t = 2

to get acceleration at 2 sec

Now find Acceleration at (1 , 3 ) interval