Aweb page designer creates an animation in which a dot on a computer screen has position ⃗r=[4 cm+(2.5cm/s 2 )t 2 ] ^ i+(5cm/s)t ^ j .

a) find the magnitude and direction of the dot’s average velocity between t=0 and t=2 s.
b) find the magnitude and direction of the instantaneous velocity at t=0, t=1 s, and t=2 s. and show the velocities calculated in pan (b).

Explanation:

a )

r = (4 + 2.5 t² )i + 5 t j

When t = 0

r₁ = 4 cm i

When t = 2s

r₂ = 14 i + 10 j

Displacement

= r₂ - r₁

=14 i + 10 j -4i

= 10i + 10j

average velocity

= displacement / time

=( 10i + 10j )/2

= 5i + 5j

b )

r = (4 + 2.5 t² )i + 5 t j

dr / dt = 5 t i + 5 j

Instantaneous velocity at t = o

(dr / dt)₀ = 5 j

Instantaneous velocity at t = 1s

(dr / dt)₁  = 5i + 5j

Instantaneous velocity at t = 2s

(dr / dt)₂ = 10i + 5 j

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.

god i hope this !