Question

Help please!!! need it asap
no wrong answers

Answer 1

Displacement at t = 0 :

• x = 4 cos(π (0) + π/4)
• x = 4 cos(π/4)
• x = 4 × 1/√2
• x = 2√2 meters

Displacement at t = 1 :

• x = 4 cos (π (1) + π/4)
• x = 4 cos (π + π/4)
• x = -4 cos(π/4) [∴ cos is negative in the interval (π, 3π/2)
• x = -4 × 1/√2
• x = -2√2 meters

Displacement between t = 0 and t = 1 :

• -2√2 - 2√2
• 
  `\boxed {-4√(2)}`

∴ The displacement between t = 0 and t = 1 is -4√2 meters.

Answer 2

`-4√(2) m`

Explanation:

Similar question to the previous one you asked, and I swear I will not make the same mistake again :)

First we will find the displacement at t = 0 and t = 1 to find both displacements.

t = 0,

`x(0)=4cos(\pi (0)+(\pi )/(4) )=4cos((\pi )/(4) )\\=4((√(2) )/(2) )\\=2√(2) m`

t = 1,

`x(1)=4cos(\pi (1)+(\pi )/(4) )=4cos(\pi +(\pi )/(4) )\\=4(-(1)/(√(2) ) )\\=-(4)/(√(2) )`

Total Displacement = Final Position - Initial Position

= x(1) - x(0)

=
`-(4)/(√(2) ) -2√(2) \\=-4√(2) m`