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
• $\boxed {-4\sqrt{2}}$

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

Answer 2

Answer:

$-4\sqrt{2} m$

Step-by-step 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,

$x(0)=4cos(\pi (0)+\frac{\pi }{4} )=4cos(\frac{\pi }{4} )\\=4(\frac{\sqrt{2} }{2} )\\=2\sqrt{2} m$

t = 1,

$x(1)=4cos(\pi (1)+\frac{\pi }{4} )=4cos(\pi +\frac{\pi }{4} )\\=4(-\frac{1}{\sqrt{2} } )\\=-\frac{4}{\sqrt{2} }$

Total Displacement = Final Position - Initial Position

= x(1) - x(0)

= $-\frac{4}{\sqrt{2} } -2\sqrt{2} \\=-4\sqrt{2} m$